Kerry cited significant progress in narrowing gaps between the two sides, but he declined to elaborate. On Thursday, aides said Kerry will remain in Amman until Friday to determine if there is additional work that requires his presence. Kerry had planned to return home Thursday.
On his sixth trip to the Middle East in as many months as America's top diplomat, Kerry met Wednesday in Jordan with representatives of the Arab League and nine of its members that support an Arab-Israeli peace plan proposed by Saudi Arabia.
In a statement after the meeting, the Arab delegation endorsed Kerry's initiative, saying his ideas "constitute a good ground and suitable environment for restarting the negotiations, especially the new and important political, economic and security elements."
The statement was significant because it could give Palestinian leader Mahmoud Abbas the political cover he would need to sell a return to negotiations to a skeptical Palestinian public.
Abbas was to convene a meeting Thursday of the PLO leadership to discuss the matter.
Kerry met with Abbas in Amman on Wednesday afternoon; they also had a lengthy working dinner Monday night.
At a news conference after the Arab League and Abbas meetings, Kerry mentioned "very wide" and "very significant" gaps between Israelis and Palestinians that had prevented the two sides from restarting talks when his efforts began several months ago.
"Through hard and deliberate, patient work, and most importantly through quiet work we have been able to narrow those gaps very significantly," he said.
"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.
Kerry refused to discuss details of the proposals he laid out to the Arab officials or how the gap with the Israelis had narrowed.
As Abbas prepared to meet with his top aides Thursday, Palestinian officials said Kerry had expressed hope that some kind of framework for doing so could be reached as early as Friday.
"The Palestinians are co-operating but it is time for the Israeli side to show the same co-operation," said the Palestinians' foreign minister, Riad al-Malki, who attended the Amman meeting.
Palestinian negotiator Mohammed Ishtayeh echoed that view.
"We are keen to see Kerry's efforts work, but so far there are no promising signs from the Israeli side," Ishtayeh said.
It was unclear whether Kerry would meet Israeli Prime Minister Benjamin Netanyahu or any of his top aides. Israel was not currently on Kerry's itinerary, although officials said that could change.
Abbas has refused to negotiate unless Israel halts all construction in West Bank settlements. Israel has refused, saying negotiations should resume without conditions. Kerry has offered the Palestinians a package of economic incentives to restart the talks.
Kerry has spent hours with Abbas and Netanyahu trying to set the stage for a return to peace talks that foundered and collapsed in 2008. Kerry insists progress has been made, but there have been few, if any, discernible signs that the two sides are getting closer to agreeing to discuss the major issues that divide them.
In addition to the peace process, Kerry was updating the Arabs on U.S. support for the Syrian opposition and attempts to convene an international conference to establish a transition government there, as well as Washington's position on Egypt's political turmoil.
Jordan's foreign minister, Nasser Judeh, said Kerry expressed concern about the economic impact the humanitarian crisis in Syria has had in Jordan, which hosts more than a half million displaced Syrians.