Story highlights Secretary of State Kerry met with Israeli, Palestinian leaders separately over 20 hours

Kerry was optimistic about progress, but Palestinian negotiator says gaps remain

Israeli Netanyahu and Palestinian Abbas want Kerry to return to work out details

Kerry wants talks to resume before the U.N. General Assembly meets in September

Secretary of State John Kerry ended four days of shuttle diplomacy Sunday without an agreement to revive Mideast peace talks but said significant progress had been made and that he would return to the region soon.

"We started out with very wide gaps and we have narrowed those considerably," he said at a news conference before leaving for Asia. "I believe that with a little more work, the start of final status negotiations could be within reach."

Kerry held more than 20 hours of meetings with Israeli Prime Minister Benjamin Netanyahu and Palestinian President Mahmoud Abbas, speaking with each of the leaders three times separately over four days. He said both asked him to return to the region in the next few weeks to finish work on a formula to restart peace talks, which have been stalled since 2010.

Despite Kerry's optimism, Palestinian chief negotiator Saeb Erekat told a news conference Sunday after Kerry's third and final meeting with Abbas, "it was a positive and profound meeting with President Abbas, but there has been no breakthrough so far and there is still a gap between the Palestinian and Israeli positions."

Kerry has revealed few details of his strategy to bring the two sides together and would not discuss Sunday the substance of the discussions or what sticking points remained.

But Israeli settlement building on land the Palestinians hope will be part of their future state remains a stumbling block. Abbas has demanded that Netanyahu halt settlement activity in the West Bank and East Jerusalem, territories captured by Israel in the 1967 war, as a precondition for beginning talks. The Palestinians also want Israel to accept the pre-1967 boundaries as a basis for a final Palestinian state.

On Saturday Netanyahu told his cabinet, "Israel is prepared to enter into negotiations without delay, without preconditions, and we are not placing any barriers on the resumption of final-status talks on a permanent peace agreement between the Palestinians and us."

Kerry left Israel for Brunei, where he was to meet with Asian leaders and hold talks with Russian Foreign Minister Sergei Lavrov about the crisis in Syria. He said he was leaving some of his staff behind to continue working with the parties.

Although Kerry said he did not want to set a deadline for resuming talks, he has said he would like then to start before the United Nations General Assembly, which has already granted de facto recognition to the Palestinians, convenes in September.

Netanyahu is concerned the Palestinians could use the U.N. session for further moves on statehood, including seeking membership in the International Criminal Court to take action against Israel. The Obama administration has threatened to cut off aid to the Palestinians if they take that route.

"One ally none of us have is time," Kerry said. "It lets patience wear thin and cynicism to solidify, and for unforeseen events to even enter into a closing window."