At the same time, many American officials have continued to insist that the best path forward with Pakistan is to work with its elected leaders and military commanders in hopes of convincing them to crack down on all militants, not just those who actively fight the government there. The Obama administration is also looking for Pakistan to help bring the Taliban to peace talks — an effort that the administration has pursued for years. As a result, officials are loath to antagonize Islamabad at a crucial moment in the war in Afghanistan.

The Afghan peace process appeared to be gaining momentum this summer with meetings between Afghan officials and Taliban representatives in Pakistan. But it was derailed by news that the Taliban’s elusive leader, Mullah Muhammad Omar, died about two years ago, and the insurgents have made significant gains in the months since. Late last month they seized a city for the first time since 2001, taking Kunduz, Afghanistan, and holding off Afghan forces for more than two weeks before pulling back.

Fearful that Afghan forces would be outmatched without American support, Mr. Obama announced last week that American troops would remain in Afghanistan through the end of his term. But after 2016, there would only be about 5,500 Americans left in Afghanistan, so the administration is eager to revive the peace process, which is expected to be on the agenda when Mr. Obama and Mr. Sharif meet on Thursday.

While Pakistan has gone after Qaeda operatives since 2001, and allowed the C.I.A. drone program to strike targets in the country’s tribal areas, it has also provided a safe haven for the Taliban and supported elements of the Afghan insurgency. Pakistan has also supported other militant groups fighting in Kashmir and targeting India.

Many in Congress fear that the F-16 jets are more useful to Pakistan in its long confrontation with India than for counterterrorism. It is unclear if Congress will approve the deal: Congress and the State Department are already in a standoff over an effort to sell used Navy cutter vessels to Pakistan earlier this year.

In March, the House Foreign Affairs Committee put a hold on about $150 million in foreign military financing — aid from the United States that foreign allies could use to purchase American weapons and other military equipment, said American officials, who spoke on the condition of anonymity because the issue has not yet been made public.

The committee said the cutters were not essential to fighting militants, the officials said. But in a letter sent in February to Secretary of State John Kerry, Representative Edward Royce of California, the committee’s chairman, and Representative Elliot L. Engel of New York, the ranking Democrat, outlined their broader concerns about Pakistan.