U.S. President Barack Obama said Thursday that he believed there was a “window of opportunity” to kickstart the Middle East peace process, after a trip to the region by Secretary of State John Kerry, AFP reports.

Speaking after a meeting with UN Secretary General Ban Ki-moon, Obama said the two “talked about Middle East peace, where there’s at least a window of opportunity for both Israelis and Palestinians to get back to the peace table.”

“We explored how the United States, as a strong friend of Israel and a supporter of the Palestinian state, can work with the United Nations and multilateral bodies to try to move that process forward,” Obama added, according to AFP.

Ban said that he hoped the region would “benefit from the momentum achieved during President Obama’s visit”, alluding to the President’s recent visit to Israel, the Palestinian Authority and Jordan.

The comments came two days after Kerry dubbed his talks with Israeli and PA leaders this week “very constructive.”

The U.S. secretary of state, however, cautioned that it was more important to find ways of resuming the long-frozen negotiations correctly rather than “quickly.”

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 not grant the PA any far reaching concessions in return for resumption of negotiations.