TEL AVIV — During a whirlwind round of diplomacy on Wednesday, Secretary of State John Kerry asserted that progress had been made on forging a cease-fire to halt the bitter fighting in Gaza between Israeli forces and Palestinian militants there led by Hamas.

“We will continue to push for this cease-fire,” Mr. Kerry said. “We have in the last 24 hours made some progress in moving towards that goal.”

But even as Mr. Kerry pressed his case with Prime Minister Benjamin Netanyahu of Israel and Mahmoud Abbas, the president of the Palestinian Authority, a defiant note was struck by one figure whom the secretary of state has conspicuously not talked with: Khaled Meshal, the political leader of Hamas.

“Everyone wanted us to accept a cease-fire and then negotiate for our rights,” Mr. Meshal said at a news conference in Qatar, his home in exile, taking aim at the very approach Mr. Kerry has sought to nurture. “We reject this, and we reject it again today.”

Mr. Kerry has emphasized that his immediate goal is to obtain a cease-fire, after 16 days of fighting that has killed nearly 700 Palestinians, 32 Israeli soldiers and three Israeli civilians.

In comments after his meeting with Mr. Abbas in Ramallah and a meeting in Jerusalem with Ban Ki-moon, the United Nations secretary general, Mr. Kerry also stressed that he hoped to lay the ground for a “sustainable” way forward after an end to the fighting.

That seemed to be a way to assure the nearly two million Palestinians in Gaza that the United States was prepared to address some of their long-term economic and political grievances without making their solution a condition for a cease-fire and to similarly acknowledge Mr. Netanyahu’s argument that any lasting political settlement should also reduce the ability of Hamas and its affiliates to attack Israel.

Mr. Kerry’s decision, however, to relegate many of these issues to a subsequent phase of the negotiations — after a cease-fire is established — also appeared to be an implicit recognition of the difficulties in resolving these issues.

“What we’re trying to figure out is how we can get to the point where the violence can stop and these bigger key issues can be addressed over the longer term,” said a senior State Department official, who asked not to be identified in keeping with the agency’s protocol for briefing reporters.

Israel’s position remained difficult. While the Israeli public has strongly supported the military’s attacks in Gaza to quell the thousands of rockets fired into Israeli territory, the government faced economic pressures on Wednesday to negotiate a halt to the war.

Because of fears of Palestinian rocket fire, the Federal Aviation Administration in Washington had extended a suspension of all United States flights to and from Israel. One rocket landed earlier in the week near Tel Aviv’s Ben Gurion Airport, the country’s main gateway. The F.A.A. lifted the restrictions effective around 11:45 Wednesday night, but said in a statement that it would “continue to closely monitor the very fluid situation around Ben Gurion Airport and will take additional actions, as necessary.”

Mr. Kerry, whose United States Air Force plane was exempt from the F.A.A. directive, flew into the airport earlier on Wednesday.

While Israel’s national carrier, El Al, added larger planes and more flights to its schedule that day to accommodate passengers stranded by cancellations, El Al was already bracing for tens of millions of dollars in losses from an enormous drop in tourist traffic this summer.