With US Secretary of State John Kerry trying to push Jerusalem and Ramallah back to the negotiating table, US officials have reportedly proposed convening a four-way summit to jump start Israeli-Palestinian peace talks in May.

Kerry met with Prime Minister Benjamin Netanyahu Saturday night and into Sunday morning, several hours after holding talks with Palestinian Authority President Mahmoud Abbas and Jordanian Foreign Minister Nasser Judeh in Amman. He is reportedly pushing a US-devised package of arrangements to pave the way for new negotiations.

A statement issued after the meeting by Kerry’s office said Israel’s recent rapprochement with Turkey would help Jerusalem with its challenges in the region.

“The reconciliation between Israel and Turkey is a very important development that will help advance the cause of peace and stability in the region,” Kerry said in the statement. He said Netanyahu and Turkish Prime Minister Recep Tayyip Erodgan “deserve great credit for showing the leadership necessary to make this possible.”

“As I discussed with Prime Minister Netanyahu this evening, this will help Israel meet the many challenges it faces in the region,” Kerry said. “We look forward to an expeditious implementation of the agreement and the full normalization of relations so Israel and Turkey can work together to advance their common interests.”

The statement cottoned to an earlier remark by Netanyahu that the conflict in Syria had been a major factor in his decision to apologize to Turkey for the deaths of nine activists aboard a blockade-busting boat in May 2010.

The meeting with Kerry came as US President Barack Obama wrapped up a four-day jaunt to the region with a trip to Petra in Jordan.

US officials have suggested the US and Jordan host four-way talks with the Palestinians and Israel in early May, Saudi paper Asharq al-Awsat reported late Saturday, citing unnamed sources. The Jordanians welcomed the idea and Kerry is following up with the Israeli and Palestinians sides, according to the paper.

Earlier in the day, Judeh told Kerry he would be happy to host talks.

Negotiations between Israel and the Palestinians have been frozen since 2010, at the tail end of a 10-month settlement moratorium. Ramallah has demanded settlement construction stop before the Palestinians will come to the table, while Israel insists on talks without preconditions.

The US has been instrumental in facilitating indirect talks between the sides, with Jordan in the past playing the role of host.

In January 2012, Amman saw a meeting between Israeli negotiator Yitzhak Molcho and Palestinian counterpart Saeb Erekat, but the session failed to bring the sides together.

On Saturday, Kerry met with Netanyahu and Justice Minister Tzipi Livni — the new ministerial overseer of Israeli-Palestinian peace efforts — along with Netanyahu’s National Security Adviser Yaakov Amidror and Molcho.

The focus of the talks was to develop new ideas for enabling a resumption of direct negotiations. Netanyahu has reportedly been considering a package of goodwill gestures – including approval of building requests, and a release of prisoners — designed to encourage Abbas to come back to the peace table.

Flush with his success in arranging Friday’s Israel-Turkey reconciliation, Kerry is hoping to be able to get Israel and the Palestinians to agree within days to new talks, Channel 10 reported Saturday night. The components: Israel will agree to release a number of Palestinian prisoners and to transfer certain West Bank areas from partial (Area B) to full (Area A) Palestinian control; the Palestinians will agree not to seek to take Israel to the International Criminal Court for alleged crimes relating to its control and policies in the West Bank.

Moves to enable a resumption of talks were reportedly discussed by Obama and Netanyahu on Friday morning, with Netanyahu detailing Israel’s security needs in the Jordan Valley under a future accord, and specifying that he wanted to see a “performance-based progression” in the talks — with measurable change on the ground as the criterion for gradual steps toward the “broad agreement” Obama said he was seeking when in Ramallah on Thursday.

During his first trip to Israel and the Palestinian Authority as president, Obama called for the resumption of peace negotiations. He offered no new plan on how to get there but said Kerry would be spending considerable time on the matter.

“Peace is necessary,” Obama said Thursday in an address to Israeli students in Jerusalem. But he was decidedly more vague about what he or his secretary of state were going to do about it. Obama’s rhetoric throughout the visit seemed to suggest that the will to achieve peace must first and foremost come from the parties themselves, and that he wants to merely assume the position of an honest broker, an interlocutor who doesn’t impose concessions on either side.

It seems that Kerry, however, is eager to engage and try to bring Israelis and Palestinians closer together, and if not reach a final agreement, perhaps an interim solution.

“Kerry very much wants to be active in this area. Obama is cautious about using his presidential political capital, but Kerry is eager to act — which is why he arrived before Obama and will leave after he goes,” Michael Herzog, a veteran of past Israeli peace negation teams, told the Global Post.

Kerry is expected to spend much time in the region in the coming weeks and months.