Israel and the Palestinians are nearly ready to resume stalled peace talks but have some particulars to work out, Secretary of State John F. Kerry said Wednesday, as he won an important Arab endorsement of terms for negotiations that fall short of long-standing Palestinian demands.

The Arab League backed Kerry’s efforts to begin a new round of peace talks without many of the conditions set by the Palestinians.

“The idea presented by Kerry is considered a suitable ground and atmosphere to start the talks, especially regarding the important political, financial and security elements,” the Arab League said in a statement issued shortly after Kerry briefed influential Arab diplomats in Jordan.

“The delegation also expressed hope that this will lead to serious talks” on establishing a Palestinian state alongside Israel and bringing a wider peace to the Middle East, the statement said.

Kerry also had his second meeting in two days with Palestinian Authority President Mahmoud Abbas, who has been reluctant to agree to terms for talks that many Palestinians see as too generous to Israel. Kerry extended his stay in Jordan in part to await the outcome of a meeting Thursday between Abbas and key members of the Palestine Liberation Organization that could decide whether the Palestinians return to the bargaining table.

“When this process started several months ago, there were very wide gaps — very significant gaps — between the two sides,” Kerry said at a news conference in Amman, but he added that the parties have narrowed those gaps “very significantly” through careful and mostly secret work.

“We continue to get closer, and I continue to remain hopeful that the sides will soon be able to come to sit at the same table,” he said. “There are still some elements, some language, that needs to be agreed upon and worked out. This is normal.”

Kerry would not give details of his discussion earlier Wednesday with members of the Arab League or further discuss how the gaps between Israel and the Palestinians were narrowed.

He has conducted most of his signature peace effort in secret, with only a handful of U.S. officials aware of the details. The rough outline of his goal is clear, however: direct peace talks between the Palestinians and the government of Israeli Prime Minister Benjamin Netanyahu that would set final borders for a Palestinian state, as well as resolve festering conflicts over the jurisdiction of Jerusalem and land claims by Palestinians and their descendants who left areas in what is now Israel when the Jewish state was formed.

The Arab League position is noteworthy because it could give Abbas the political protection he needs to sell talks to skeptical Palestinians and members of his government. The statement has the support of many of the PLO’s largest donors and political backers.

Abbas wants a halt to all Israeli settlement construction in the West Bank and the release of Palestinian prisoners before he will negotiate. Kerry and Netanyahu have argued that those terms are unrealistic and should be part of the discussions.

Kerry is making his sixth trip to the region in five months, almost all focused on peace talks. He is not expected to visit Israel this time, and the State Department has played down speculation of an announcement of new talks.

Kerry is trying to close a deal he saw as within reach on his last visit, in June, when a whirl of shuttle diplomacy failed to produce a date for talks to resume after a hiatus of nearly five years. An attempt to restart talks in 2010 sputtered after only a few days.

His efforts have been overshadowed by the more immediate crises in Syria and Egypt, but the secretary argued Wednesday that the more than six decades of enmity between Israel and the Palestinians lies at the heart of the broader volatility in the Middle East.

He said he knows there is widespread skepticism that his peace initiative can work after so many years and so many failed attempts.

“The easiest bet among Middle East prognosticators has always been on predicting impasse,” Kerry said. “I understand that. But I also know that through the efforts that are being made now, the best hope for a different outcome is to have a quiet process that is working the way the parties are working now.”

Ahmed Ramadan in Beirut contributed to this report.