Top US diplomat John Kerry met Israeli Prime Minister Benjamin Netanyahu on Tuesday on the third day of talks seeking to piece together a plan to persuade Israelis and Palestinians to return to negotiations.
Speaking to reporters late on Monday, Kerry said he was pursuing a "quiet strategy" for ending decades of mistrust between the two sides, who have not met for direct talks since September 2010.
He refused to give specifics, but indicated that one area of focus was trying to build up the teetering Palestinian economy.
Kerry said movement in areas such as the economy "could be critical to changing perceptions and realities on the ground, all of which can contribute to forward momentum."
Netanyahu and Kerry met at David's Citadel Hotel in Jerusalem on Tuesday morning, after "very productive" dinner talks late on Monday.
"I think it's fair to say we made progress," he said.
The two leaders had agreed "to do some homework" over the next few weeks "with a view to seeing how we can really pull all of the pieces together," he told reporters, praising Netanyahu for his "good faith efforts".
"I'm determined not only to resume the peace process with the Palestinians, but to make a serious effort to end this conflict once and for all," Netanyahu said.
For Israel, questions of "recognition and security" were key issues, he said in a reference to Palestinian recognition of Israel as a Jewish state.
Kerry is scheduled to leave for London at around 1100 GMT where he will attend a meeting of G8 foreign ministers.
Israel's top-selling Yediot Ahronot said Kerry was hoping to get Israel and the Palestinians to sit down in Amman for four-way talks with the United States and Jordan.
And the Al-Quds daily said Jordan was to be involved as a key player in negotiations over over the status of Jerusalem, which Israel claims as its capital while the Palestinians want the annexed eastern sector as capital of their future state.
There was no immediate confirmation of either report, but Jordan has been a key player in the peace process since it signed a peace treaty with Israel in 1994.
Momentum is also gathering among Arab nations to revive the stalled peace process, with a delegation from the Arab Peace Initiative (API) committee to visit Washington later this month.
The 2002 Arab Peace Initiative, first proposed by Saudi King Abdullah, offers pan-Arab diplomatic recognition of Israel in return for an end to the occupation and the establishment of a Palestinian state.
Palestinian president Mahmud Abbas attended a meeting of the API committee in Doha on Monday, a day after he held talks with Kerry at his West Bank headquarters in Ramallah.
During the meeting, Abbas told Kerry the release of prisoners held by Israel was a "top priority" for resuming peace talks, his spokesman said.
Abbas also wants Netanyahu to present a map of the borders of a future Palestinian state before talks can resume.
The Palestinian leader has repeatedly made clear there would be no return to negotiations without a settlement freeze, but he has also made it known he would suspend for two months all efforts to seek international recognition of a Palestinian state to give US-brokered efforts a chance.
But Netanyahu has rejected any return to the 1967 lines and on Monday a high-ranking political official told Maariv newspaper that presenting a map was out of the question.
Meanwhile, Israel's army radio said US Defence Secretary Chuck Hagel is due to visit Jerusalem on April 21 at the invitation of Defence Minister Moshe Yaalon on his first trip to the region since taking over as Pentagon chief.
Topping the agenda will be the issues of Iran's nuclear programme and the crisis in Syria, the radio said.
In a separate development, Turkey delayed talks with Israel over compensation the Jewish state will pay to the families of victims of a deadly 2010 raid on a Gaza-bound flotilla, in a blow to Kerry's diplomatic efforts.
The two countries recently patched up a nearly three-year diplomatic rift after Israel apologised and pledged to pay compensation.
Talks had been due to begin on April 12, but were pushed back to April 22, an Israeli official said, citing "logistical reasons."
Speaking in Istanbul on Sunday, Kerry pushed the two to restore full diplomatic relations, saying Ankara could play a "central" role in the peace process.