UN Secretary General Ban Ki-moon said Israeli-Palestinian talks should lead to a peace agreement within 24 months.
Senior US, EU and Russian officials have met Mr Ban in Moscow to try to push forward the stalled talks.
They come amid tension over Israel's announcement of new settler homes in East Jerusalem.
Israeli PM Benjamin Netanyahu informed Washington of new confidence-building measures on the eve of the meeting but no details have been given.
 |  [Mrs Clinton and Mr Netanyahu] discussed specific actions that might be taken to improve the atmosphere for progress toward peace  PJ Crowley US State Department  |
But events in the Middle East on Thursday highlighted the difficulties the Quartet faces.
A rocket fired from the Gaza Strip killed a Thai agricultural worker when it hit an Israeli kibbutz.
Israeli aircraft attacked up to six targets in Gaza overnight but there were no reports of any serious casualties.
The violence came as the EU's new foreign policy chief, Baroness Ashton, visited Gaza - one of the highest-level visits there by a Western official since the Palestinian Islamist group Hamas took power.
Lady Ashton is attending the talks in Moscow.
Significant conversation
No details were given of Thursday's telephone conversation between Mr Netanyahu and US secretary of State Hillary Clinton, who is now in Moscow.
 Tensions are high over Israel's new settlement plans |
But their call is significant, the BBC's Kim Ghattas reports from the Russian capital.
Enough progress was apparently made for George Mitchell, Washington's Middle East envoy, to travel to the region this weekend. He had postponed an earlier trip amid the settlement row.
"They discussed specific actions that might be taken to improve the atmosphere for progress toward peace," US state department spokesperson PJ Crowley said in Moscow.
It is likely this means a goodwill gesture by the Israelis, like the release of Palestinian prisoners, our correspondent says.
Mr Crowley added that Washington would now review the prime minister's response and work with Israelis and Palestinian to keep the indirect negotiations, known as proximity talks, moving forward.
Washington wants those talks to focus on the core issues at the heart of the conflict, like borders and Jerusalem, our correspondent says.
