KUWAIT CITY, 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 with Israeli and Palestinian leaders amid increasing talk of a possible breakthrough that could return the two sides to the negotiating table after years of stalemate.

Kerry stressed he was not setting a firm deadline for resuming peace talks, but he stressed the importance of making headway before the United Nations General Assembly resumes its debate over the Middle East in September.

“Time is the enemy of a peace process,” Kerry said.

After three months of intensive effort by 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 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.

The Palestinians have repeatedly set and extended deadlines for 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 Kerry tries to reignite talks.