US President Barack Obama has called on Israeli and Palestinian leaders to act with a "sense of urgency" in restarting stalled peace talks.
Mr Obama was speaking in New York where he was hosting tri-lateral talks between leaders from both sides.
US Middle East envoy George Mitchell later said resolving the settlement issue was not a precondition for talks.
He said "many obstacles" remained but that substantial progress had been made in resolving contentious issues.
The meeting brought Israeli Prime Minister Benjamin Netanyahu and Palestinian leader Mahmoud Abbas together for the first time since Mr Netanyahu came to office in March.
Mr Obama - who has defined peace between Israel and the Palestinians as a "national interest" of the US - first met each leader separately in what he described as "frank but productive" talks, before hosting the trilateral meeting.
“ We have substantially and significantly progressed in reducing the number of issues on which there is disagreement ”
"Permanent status negotiations must begin and begin soon," he said. "It is past time to talk about starting negotiations. It is time to move forward."
In a news conference later, Mr Mitchell said the meeting had been "cordial" and at times "blunt", but that Mr Netanyau and Mr Abbas had "recognised the urgency of moving promptly".
He said that while no agreement had yet been reached on the issue of Israeli settlement building in the West Bank and East Jerusalem, there were no preconditions for talks to restart.
Jeremy Bowen, BBC Middle East editor
The streets around the Waldorf Astoria Hotel, where the meetings were being were brought to a standstill by motorcades and security. Unfortunately for President Obama his hopes for the Middle East are gridlocked too. He planned to use the UN General Assembly this week to inaugurate a brand-new peace process with the aim of giving the Palestinians independence alongside Israel. But the two sides are very far apart. There is tension now in the relationship between President Obama and Prime Minister Netanyahu. This Israeli government has delivered the White House a humiliating rebuff. Palestinian President Mahmoud Abbas, on the other hand, is doing more or less as the US asks, but, if negotiations did begin, there are serious doubts about whether he could deliver on any deal he made.
"Our objective all along has been to re-launch meaningful final status negotiations in a context that offers the prospect of success," he said.
"We have substantially and significantly progressed in reducing the number of issues on which there is disagreement and we hope to complete that process in the near future."
Israel has repeatedly rejected US and Palestinian demands for a total freeze on settlement building.
Speaking after the talks, Mr Netanyahu said there had been a "general agreement that the peace process should resume as soon as possible with no preconditions".
Mr Abbas said he had called on Israel to respect the road map to peace and withdraw to its internationally-recognised 1967 borders.
Mr Obama had hoped to launch new talks at the UN General Assembly, but it appears his hopes for peace in the Middle East remain gridlocked, says the BBC's Jeremy Bowen in New York.
Prior to the meeting, the White House had been keen to play down hopes, saying it had no "grand expectations".
Israeli and Palestinian participants had also said they did not expect many concrete developments.
Israeli government secretary Zvi Herzog said the talks were "a step in the right direction", but that conditions were "not ripe for a formal re-launch of negotiations".
Last week, a senior Palestinian official suggested his side was taking part so as not to disappoint the US and that doing so did not mean a resumption of peace talks.
The negotiating process was suspended in December.
Disagreements over the settlements issue have blocked all attempts to restart the peace talks so far.
US and Palestinian negotiators have said Israel must fully halt work on the construction of settlements in the West Bank before a new round of peace talks can take place, something Israel has refused to do.
Mr Netanyahu had previously offered a temporary freeze for several months, but not in East Jerusalem or in cases where homes had already been approved.
He argues that the "natural growth" of settler families must be accommodated.
Hamas, Mr Abbas's rivals who control Gaza, condemned the talks as "cover for Israeli aggression", while Israeli settlers opposed to a settlement freeze set up a protest tent in Jerusalem.
Separately, the Israeli prime minister said he would boycott the address by Iranian President Mahmoud Ahmadinejad to the UN General Assembly because of his views on the holocaust.
Also on Tuesday, an Israeli-Arab man was shot dead in the West Bank after he tried to run over Israeli soldiers, the military said.
A neighbour of the man told the Associated Press he had had no connection with armed groups and was killed "in cold blood".