George Mitchell, the top US envoy to the Middle East, said on Sunday that he aimed to finalise a deal with Israel on a freeze of Jewish construction in occupied Palestinian territory this week to help revive peace talks.

Mr Mitchell, who spoke following a meeting in Jerusalem with Shimon Peres, the Israeli president, said: “While we have not yet reached agreement on many outstanding issues, we are working hard to do so, and indeed the purpose of my visit here this week is an attempt to do so.”

The meeting took place just hours after the Israeli president was discharged from a hospital, a day after fainting on stage during a public appearance.

Washington appears to be racing to conclude a settlements pact with Israel ahead of the UN General Assembly due to take place late next week. Barack Obama, the US president, is expected to try to convene a tripartite meeting on the sidelines of the event with Benjamin Netanyahu, the Israeli premier, and Mahmoud Abbas, president of the western-backed Palestinian Authority.

However, the chances of such a meeting are uncertain as Mr Abbas has said he will not participate unless Israel institutes a total construction moratorium.

According to the Israeli press, a freeze may last for about nine months and is unlikely to include mostly Arab east Jerusalem. Palestinians want east Jerusalem as the capital of their future state, while Israel views the whole of Jerusalem as its undivided capital.

On Sunday, Mr Netanyahu signalled that a breakthrough in the settlements negotiations may not be imminent. Speaking to reporters before the weekly cabinet meeting, he said: “There is still work to do. We have made progress on certain items, and there are also certain items on which we have yet to make progress. I hope that we will succeed in reducing the gaps.”

Mr Netanyahu spoke just hours before he was due to travel to Cairo to meet with Hosni Mubarak, the Egyptian president, for the second time since taking power in late March. The two leaders are expected to discuss the settlements talks as well as Egyptian efforts to facilitate a prisoner swap between Israel and Hamas, the Islamist group that rules the Gaza Strip, where it has held a kidnapped Israeli soldier since 2006.

Mr Mitchell is scheduled to meet Mr Netanyahu on Monday and travel to the West Bank city of Ramallah on Tuesday to see Mr Abbas.