Israel’s president says Trump asked him to pardon Netanyahu, who has not been convicted.

“I hereby call on you to formally pardon Benjamin Netanyahu, who has been a formidable and decisive War Time Prime Minister, and is now leading Israel into a time of peace,” Mr. Trump wrote in a letter to Mr. Herzog, whose office released it.

Mr. Trump has called for Mr. Herzog to pardon Mr. Netanyahu on several occasions, though the letter is a more formal request. The White House did not immediately respond to a request for comment.

People seeking clemency in Israel have to formally request it, either themselves or through a designated representative like an attorney. Mr. Netanyahu did not formally ask for a pardon, Mr. Herzog’s office said, and Mr. Trump’s letter did not appear to meet that standard.

Mr. Netanyahu has been on trial since 2020 on counts of fraud, bribery and breach of trust by a public official. He has denied all of them and denounced his prosecutors as having launched a politically motivated “witch hunt.”

The corruption charges have split the Israeli public. Centrists and leftists have criticized Mr. Netanyahu as tarred by allegations of abuse of public office, while his defenders consider him a historic statesman targeted by a leftist judicial deep state.

It comes as the House crawls back to life with an agenda that is much the same as it was when the chamber last convened on Sept. 19, and Republicans passed a plan to temporarily fund the government. Then, Speaker Mike Johnson called an indefinite recess, arguing that there was no reason for the House to meet until Senate Democrats accepted his party’s proposal.

For weeks, the House lay mostly dormant, with no legislation considered, no hearings held and no debate on the floor. While the representatives went on break — one they have been quick to frame as working from home rather than a nearly two-month vacation — hundreds of thousands of federal workers went without pay, millions of low-income Americans wondered whether they would receive food assistance and exasperated air travelers dealt with disruptions.

Mr. Johnson, who has held near-daily news conferences at the Capitol during the shutdown, is hoping that the House will quickly take up and pass the Senate’s measure to reopen the government.

That legislation, passed on Monday, would fund the government through Jan. 30 and includes spending bills that cover programs related to agriculture, military construction, veterans and legislative agencies for most of next year. The measure also includes a provision that would restore the jobs of federal workers who were laid off during the shutdown and guarantee back pay for those who were furloughed.

But several challenges may lie in store. Mr. Johnson presides over a very slim majority. He must keep Republicans largely united around the spending package, given the nearly solid opposition of Democrats who are livid that it fails to meet their chief demand of extending federal health care subsidies set to expire at the end of the year.

Mr. Johnson, who routinely leans on Mr. Trump to help him corral his fractious rank and file for close votes, has stressed that the spending legislation is a priority of the president, who has indicated that he would sign it. So far, a group of fiscal conservatives who ideologically oppose stopgap spending bills appear to be on board. Still, at several points, members of that group have thrown up unexpected roadblocks, and Mr. Johnson may have to contend with their complaints.

Given the prospect of a tight vote, Mr. Johnson is also likely to need every Republican member to return. Action, which House leaders have said may begin late Wednesday afternoon, could be delayed as lawmakers contend with the mounting air travel problems that have been one of the most visible consequences of the shutdown fight.

Democrats — who have returned to the Capitol in large groups at various points throughout the shutdown — are hoping to limit defections to increase the pressure on Republicans. Representative Jared Golden of Maine backed the G.O.P. plan in September and is likely to do so this week, while Henry Cuellar of Texas, has said he supports reopening the government quickly.

Democrats’ ranks will be bolstered after Mr. Johnson swears in Representative-elect Adelita Grijalva, the Arizona Democrat who was elected seven weeks ago, whom he had refused to seat.

Citing precedent, the speaker declined to swear her during a House recess that he called and prolonged.

Democrats have cried foul, pointing to Ms. Grijalva’s pledge to add her name to a bipartisan petition to force a vote on a measure demanding that the Trump administration release files connected to the deceased sex offender Jeffrey Epstein.

As it stands, Ms. Grijalva would provide the last necessary signature for the petition, which the White House opposes, to move ahead. That will create another headache that Mr. Johnson and Republican leaders will have to contend with in the weeks ahead.

The delay prevented Ms. Grijalva from freely entering and moving about the Capitol complex, or having access to the budget or the materials she needed to do her job. As recently as Tuesday afternoon, she told NPR that she had not heard directly from Mr. Johnson’s office about the swearing-in and that she was “90 percent” confident it would happen at last. She said on social media on Monday that she was traveling to Washington after hearing from news reports and Representative Hakeem Jeffries, the minority leader, that she could soon be seated.

“For seven weeks, 813,000 Arizonans have been denied a voice and access to basic constituent services,” Ms. Grijalva said. “This is an abuse of power that no Speaker should have.”

For weeks, Mr. Johnson had justified his refusal by saying he could not and would not seat Ms. Grijalva while the House was out of session. There is no such rule in the chamber that would block the swearing-in of a duly elected member of Congress. Though Mr. Johnson had so far kept the House out of session, the chamber can operate even in the event of a government shutdown, and he swore in two Florida Republicans who won special elections earlier this year while the House was in recess.

As a member of Congress, Ms. Grijalva would narrow the slim majority that Republicans hold in the House. She has also vowed to provide the last necessary signature on a bipartisan petition that would force a floor vote on a measure demanding the Justice Department release its files on the deceased sex offender Jeffrey Epstein. Democratic lawmakers have seized on Ms. Grijalva’s pledge in trying to shame Mr. Johnson into abiding by his duty to swear her in.

Mr. Johnson has claimed his refusal to seat Ms. Grijalva had nothing to do with avoiding the floor vote. Democrats, including Senator Ruben Gallego of Arizona, insisted he was “covering up for pedophiles.”

“In my conversations with the airlines and with the F.A.A., and what we’re seeing with air traffic controllers — we feel there’s going to be significant issues in the airspace,” Mr. Duffy said, referring to the Federal Aviation Administration, at a news conference at O’Hare International Airport in Chicago.

If the government does not open soon, he added, “you might have airlines that will say, ‘We’re going to ground our planes. We’re not going to keep flying anymore,’” predicting that such a disruption could happen even before the Thanksgiving travel rush, perhaps as soon as this weekend.

Throughout the shutdown, Mr. Duffy has warned of impending chaos, drawing rebukes from Democrats that his forecasts were more about pressuring them to end the shutdown than offering impartial assessments of the air-travel system.

Last week, Mr. Duffy and the F.A.A. ordered mandatory flight reductions at 40 airports nationwide. The cuts, which began with a 4 percent reduction on Friday and were slated to rise to 10 percent by the end of the week, were based on the F.A.A.’s analysis of data, Mr. Duffy has said, and were imposed to alleviate strain on air traffic controllers, who have been increasingly struggling with absences in their ranks.

On Tuesday, Mr. Duffy said he would reverse the restrictions only if that data — which includes the frequency of close calls between planes and of delays forced by shortages of air traffic controllers — improved.

Controllers have been forced to work without pay through the shutdown, and have missed two full paychecks since the funding lapse began. The lack of pay has accelerated retirements, Mr. Duffy said, and has forced some newer controllers with lower salaries and smaller savings accounts to seek outside income.

The resulting shortfall of controllers led to an uptick in delays caused by low staffing, known as staffing triggers, at some control towers, according to Mr. Duffy and the controllers’ union, exacerbating already crippling problems. For years, most certified controllers have been forced to work overtime to compensate for vacancies in more than 20 percent of their positions.

Last weekend, a high number of staffing triggers — 81 on Saturday alone — signaled how much worse it could get if the shutdown dragged into the busy Thanksgiving holiday travel season. But on Tuesday, there were signs of marked improvement, Mr. Duffy said, with only four staffing triggers as of 4 p.m.

“I think our air traffic controllers are seeing an end to the shutdown and are feeling more hopeful,” Mr. Duffy said, adding, “If the House does their work tomorrow, I think we’re well on our way to getting to more normal air travel, less cancellations.”

Mr. Duffy said that air traffic controllers would receive approximately 70 percent of their missed pay within 24 to 48 hours of the shutdown ending, and the rest within a week. He also endorsed President Trump’s proposal, issued on social media on Monday, to reward controllers who never missed a shift during the shutdown with a $10,000 bonus.

“Brilliant,” Mr. Duffy said of Mr. Trump’s proposal, adding that perhaps the controllers with perfect attendance “should come to the White House and he should present them with their checks.”

But Mr. Duffy did not endorse Mr. Trump’s simultaneous exhortation to air traffic controllers who had missed shifts during the shutdown to quit.

“I’m trying to bring more air traffic controllers in,” Mr. Duffy said. “I’m not trying to take controllers out.”

He said he reserved his concern for controllers who called in sick before even missing a first paycheck. “I’m concerned about their dedication,” Mr. Duffy said, adding: “If we have controllers who were systemically not doing their job, we will take action.”

Last week, a federal judge in Illinois, Sara L. Ellis, restricted the Border Patrol’s use of crowd-control weapons, saying, “The use of force shocks the conscience.” She also ordered agents to wear body cameras.

In response to questions on Tuesday about the planning for operations in Charlotte and New Orleans, Tricia McLaughlin, an assistant secretary at the agency, said she could not discuss “future or potential operations.” She added, “Every day, D.H.S. enforces the laws of the nation across the country.”

On Tuesday, officials in New Orleans and Charlotte did not respond to requests for comment on the potential deployments. President Trump has repeatedly indicated that he plans to establish a federal presence in New Orleans, citing “a crime problem,” and Louisiana’s Republican governor, Jeff Landry, has asked him to deploy the National Guard in the state.

The brutal killing in August of Iryna Zarutska, a 23-year-old riding a light rail train in Charlotte, inflamed conservatives, who cited the episode as a prime example of disorder in Democratic-run cities.

In Charlotte, violent crime has decreased by 20 percent since last year, according to the police department.

Crime rates have also declined significantly in New Orleans over the past several years.

Eduardo Medina contributed reporting