KUWAIT — Secretary of State John Kerry said Wednesday that progress toward a Middle East peace agreement needed to be made before September, as he headed for a fifth trip to the region amid increasing talk of a possible breakthrough that could return Israeli and Palestinian leaders to the negotiating table after years of stalemate.

Mr. Kerry stressed that he was not setting a firm deadline for resuming peace talks, but repeated his argument that time was an enemy of his push for a comprehensive agreement and stressed the importance of making headway before the United Nations General Assembly resumes its debate over the Middle East in September.

“Long before September we need to be showing some kind of progress in some way because I don’t think we have the luxury of that kind of time,” he said in a joint news conference with his Kuwaiti counterpart.

“Time is the enemy of a peace process,” Mr. Kerry said. “The passage of time allows a vacuum to be filled by people who don’t want things to happen.”

After three months of intensive effort by Mr. Kerry, anticipation has been building in Jerusalem and the West Bank that this time, he would bring with him a concrete proposal that might move the ball. Israeli news reports over the last two days have suggested new flexibility by President Mahmoud Abbas of the Palestinian Authority and Prime Minister Benjamin Netanyahu, as both sides grow more worried about being blamed if Mr. Kerry’s push fails to show progress. But while experts on the peace process see growing momentum around Washington’s initiative, they cautioned that getting the parties back to the table was only a first step.

“Kerry is not giving up,” Gershon Baskin, co-chairman of the Israel-Palestine Center for Research and Information, said in an interview. “The question is where does it go after that, because each side is going to confront their own political public inside their own camps, and they’re going to face difficulties moving forward.”

Mr. Kerry acknowledged the uphill battle but described Mr. Netanyahu and Mr. Abbas as skilled politicians who understood that the stakes in resolving the conflict were "bigger than any one day or one moment," and "certainly more important to their countries than some of their current political challenges may make it seem.”

“I wouldn’t be here now if I didn’t have a belief that this is possible,” Mr. Kerry added. “But this is difficult.”

Kuwait was the fourth stop on Mr. Kerry’s eight-nation trip, which is mainly devoted to the Israeli-Palestinian conflict and the crisis in Syria.

As a senator, Mr. Kerry voted against the resolution in 1990 that authorized force to evict Iraqi forces from Kuwait. But that debate appeared to have been long forgotten as he had a lengthy meeting with the Kuwaiti emir, Sabah al-Ahmed al-Jaber al-Sabah, and other senior officials.

Kuwait’s foreign minister, Sheikh Sabah Khalid al-Hamad al-Sabah, reiterated his country’s interest in transferring two Kuwaiti prisoners in the American prison in Guantánamo Bay, Cuba, to Kuwaiti custody, adding that Kuwait was willing to provide guarantees that they would brought before a domestic court. Mr. Kerry said that President Obama wanted to close the Guantánamo facility and the White House would study the Kuwait request.

Mr. Kerry’s next stop is Jordan, where he is scheduled to have three days of meetings with Israeli, Jordanian and Palestinian officials.

The Palestinians have repeatedly set and extended deadlines for Mr. Kerry’s efforts, with a threat that they would leverage the observer-state status they won in the United Nations last fall to seek to prosecute claims against Israel in the International Criminal Court. The Israelis have quietly agreed not to begin new settlement projects in the West Bank while Mr. Kerry tries to reignite talks, though they have allowed already-approved housing units to advance toward constructions.

Israeli news reports this week have laid out a variety of scenarios for a breakthrough. One said the chief Israeli and Palestinian negotiators would meet under American auspices in Amman next week, something Mr. Kerry denied in his news conference. Another said Mr. Abbas had agreed to enter direct talks with Mr. Netanyahu for a limited time, dropping his demand that Israel first accept the pre-1967 borders with minor adjustments as the starting point. A third said Israel would release 120 Palestinians who have been in Israeli prisons for more than 20 years as Ramadan begins July 8.

Palestinian leaders denied the reports, saying they were Israeli “spin” and “trial balloons.”

“These are just speculations,” Saeb Erekat, the chief Palestinian negotiator, said Tuesday."Let’s wait for Kerry to come and then we can talk.”

Mr. Abbas repeated on Wednesday his frequent statement that he would return to talks if Israel accepted the 1967 borders. Mr. Netanyahu, for his part, said Tuesday that talks must be sustained, not time-limited, and that Israel was not simply trying to check a box “to show that we’ve begun negotiations.”

“Our goal is to persist in the negotiations, to engage in them consistently over a serious period of time in order to try to grapple with all the issues, and come to an agreement that resolves the fundamental issues in the conflict,” Mr. Netanyahu said. “This will require time, determination and a systematic approach.”

Several Israeli experts on the peace process said that both sides were maneuvering publicly and privately to avoid being blamed for a failure to revive talks.

Mr. Abbas “can’t be backed into a corner again and have people say the Palestinians are the naysayers,” said Mr. Baskin, a veteran negotiator who remains in close contact with the Palestinian leadership. “By saying we’re going in for a limited time to evaluate the seriousness of Israel will be enough for him to explain it to the Palestinian public.”

But Mr. Baskin was one of several analysts who expressed doubt that a new, publicly heralded round of talks would yield much, given the deep divisions and pressures each leader faces in his own political house.

“Almost everybody who’s been professionally involved in the peace process does not believe that a permanent status agreement is possible at this time,” cautioned Dore Gold, a former Israeli negotiator and aide to Mr. Netanyahu who is now president of the Jerusalem Center for Public Affairs. “What is needed is a new paradigm in order to make this work, but there’s no indication that any new ideas are surfacing.”