U.S. Secretary John Kerry on Tuesday wrapped up three days of what he termed “very constructive” talks with Israeli and Palestinian Authority leaders, AFP reported.

Speaking to reporters shortly before leaving for London, a cautious Kerry said it was more important to find ways of resuming the long-frozen negotiations correctly rather than “quickly.”

His Jerusalem and Ramallah stopover was the second leg of a 10-day trip which will also take him on his first visit to Asia since taking over as Washington’s top diplomat.

During the visit, Kerry met Palestinian Authority Chairman Mahmoud Abbas and then Israeli Prime Minister Binyamin Netanyahu, in pursuit of what he called a “quiet strategy” for ending decades of mistrust between the two sides, who have not held direct talks since September 2010.

“Each of them made very serious and well-constructed suggestions with respect to what the road forward might look like,” he told reporters at the Ben Gurion airport just before leaving, according to AFP.

But “doing it right is more important than doing it quickly,” he said.

On Monday night, Kerry held “very productive” dinner talks with Netanyahu and the two met for a second time early Tuesday.

“We made progress … and each of us agreed to do some homework” with the aim of “seeing how we can really pull all of the pieces together,” he said as Netanyahu reaffirmed his commitment to return to talks.

“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, noting the key issues of security and of recognition by the PA of Israel as a Jewish state.

Kerry said the two had discussed “specific steps we could take to break the red tape” hampering the economic growth in the PA, a move he said would ultimately improve Israel’s security.

In parallel to Kerry’s efforts, Arab states are also seeking ways of reviving peace moves.

Abbas attended a meeting of the Arab Peace Initiative (API) committee in Doha on Monday.

First proposed in 2002 by Saudi King Abdullah, the API offers Arab diplomatic recognition of Israel in return for its complete withdrawal from Judea and Samaria and a resolution of the “Palestinian refugee” issue.

Kerry admitted the API might not suit as a basis for negotiations “in its current format,” reported AFP, but added that “any document where you have a proposal for peace and you have a dozen Arab countries willing to make peace… (is) an important contribution to the dialogue.”

Abbas told visiting Kerry on Sunday that Israel should freeze construction in Judea, Samaria and eastern Jerusalem and release terrorist prisoners, especially those arrested before the 1993 Oslo Accords, before any resumption of peace talks.

Abbas also wants Israeli Prime Minister Binyamin Netanyahu to present a map of the borders of a future Palestinian state before talks can resume, according to a report last week, but a top political official told the Maariv daily newspaper this was out of the question.

Israeli officials told Kol Yisrael radio on Tuesday that they doubt the U.S. will succeed in persuading the PA to return to negotiations, despite Kerry’s resolute effort to do just that.

The sources said that the PA’s demand to get a map of the final borders Israel wants to attain is unacceptable, and added that Israel will no grant the PA any far reaching concessions in return for resumption of negotiations.