AMMAN, Jordan — Israeli and Palestinian leaders have “established a basis” to resume direct peace negotiations for the first time in three years, Secretary of State John Kerry announced Friday, after an intense round of shuttle diplomacy aimed at reviving the dormant Middle East peace process.

The preliminary agreement is the Obama administration’s first incremental success in efforts to convene talks since the president’s attempt to broker a deal early in his first term ended in acrimony. If negotiations develop beyond what Mr. Kerry described as an “initial” phase by chief negotiators, it would be the first face-to-face meeting of Prime Minister Benjamin Netanyahu of Israeli and President Mahmoud Abbas of the Palestinian Authority since the Arab Spring upended politics across the Middle East.

After multiple, marathon sessions with each man in recent weeks, Mr. Kerry said here Friday that both had shown “courageous leadership” that made him “hopeful” about the prospects for resolving the intractable conflict. He said that if “everything goes as expected,” Saeb Erekat, the chief Palestinian negotiator; Tzipi Livni, the Israeli minister in charge of the peace process; and Isaac Molho, Mr. Netanyahu’s special envoy, would join him for talks in Washington “within the next week or so.”

“The representatives of two proud peoples today have decided that the difficult road ahead is worth traveling and that the daunting challenges that we face are worth tackling,” Mr. Kerry said in Amman, the Jordanian capital, on Friday night before flying back to Washington. “They have courageously recognized that in order for Israelis and Palestinians to live together side by side in peace and security, they must begin by sitting at the table together in direct talks.”