The US envoy to the Middle East, George Mitchell, will hold talks tomorrow with Binyamin Netanyahu, despite the Israeli prime minister's formal rejection of White House demands for a freeze on Jewish settlements in East Jerusalem.

Both the US and the Palestinians are calling for a halt on construction as a precondition for a resumption of peace talks with Israel. But according to Israeli officials, Netanyahu wrote to Barack Obama at the weekend rejecting the demand.

Today Netanyahu told Israel's Channel 2: "I am saying one thing. There will be no freeze in Jerusalem. There should be no preconditions to talks."

Relations between Israel and the US sank to a new low last month after a tense meeting in Washington in which Obama gave Netanyahu an ultimatum to respond to US calls for a freeze.

After a lengthy delay that will have further irritated the White House, Netanyahu responded at the weekend, aides told Associated Press and the Wall Street Journal.

Tension between the US and Israel resulted in Mitchell putting on hold for a month his shuttle diplomacy between the Israelis and Palestinians. He arrived in Israel today and is due to resume diplomatic efforts tomorrow, combining his talks with Netanyahu with a trip to Ramallah to see the Palestinian president, Mahmoud Abbas. Saeb Erekat, the chief Palestinian negotiator, said he hoped Mitchell would bring the right formula to allow indirect talks to start.

Although Netanyahu ruled out a halt on settlement-building, he was reported to have offered other proposals as concessions to the Palestinians. There was media speculation in Israel that Netanyahu may have publicly ruled out a freeze but will privately impose one.

Earlier this week General James Jones, Obama's national security adviser, expressed disappointment that direct negotiations between the Israelis and Palestinians had not yet begun. He said it was "time to begin those negotiations and to put an end to excuses".

Obama's Middle East adviser, Dan Shapiro, is also in Israel, another sign that, in spite of the reported rejection by Netanyahu, negotiations are continuing behind the scenes.

Mark Regev, a spokesman for Netanyahu, would not discuss the details of Israel's talks with the US administration but he said: "We want this process to succeed and to see the restart of talks. We hope that this is possible soon."

There have not been direct peace negotiations between the two sides since before Israel's war in Gaza early last year.

Israel claims sovereignty over East Jerusalem, which it captured in the 1967 war and later annexed, and Netanyahu has insisted construction must continue there. Internationally, East Jerusalem is regarded as under Israeli military occupation and settlement on occupied land is illegal under international law.

"It is just impossible and unacceptable that people try to impress us that we should limit construction in Jerusalem," said Benny Begin, a senior cabinet minister.

The US administration spent much of last year trying to convince Netanyahu to halt all settlement construction. Netanyahu refused and agreed only to a 10-month partial halt to construction in the West Bank – a moratorium which expires this autumn. Mitchell then spent many months trying to prepare indirect negotiations between Israel and the Palestinians, but a day after an agreement on so-called "proximity talks" was announced, Israeli officials gave approval for 1,600 new homes in an East Jerusalem settlement during a visit by the US vice-president, Joe Biden. Biden condemned the decision and the indirect talks collapsed before they had begun.

Israel has yet to restore its relations with the US and a refusal by Netanyahu to halt East Jerusalem settlement building would only prolong the confrontation. However, the Wall Street Journal said Netanyahu would offer other incentives instead, including the release of Palestinian prisoners from Israeli jails, the lifting of some checkpoints in the occupied West Bank and allowing some more goods to enter Gaza, despite the long Israeli economic blockade.

Several US officials have emphasised the importance for the US of progress in Israeli-Palestinian peace negotiations. Jones indicated this week that progress in the Middle East would help Washington curb Iranian nuclear ambitions. "Advancing this peace would … help prevent Iran from cynically shifting attention away from its failures to meet its obligations," he said.

Israel has long argued that confronting Iran ought to be an international priority. But Avigdor Lieberman, the Israeli foreign minister, this week resisted any suggestion that a peace agreement should be imposed on Israel and the Palestinians.

"Any attempt to force a solution on the parties without establishing the foundation of mutual trust will only deepen the conflict," Lieberman told diplomats in Jerusalem.

Envoy's troubles

A high point in the lives of Tony Blair and former US senator George Mitchell was their successful negotiation, against the odds, of the Northern Ireland peace process in 1997.

The two have worked together again for more than a year, trying to resolve the Israeli-Palestinian conflict, Mitchell as Barack Obama's special envoy to the Middle East and Blair as the representative of the Quartet, comprising the US, UN, EU and Russia. Both are finding the Middle East harder to crack – so hard that for months there have been rumours on the diplomatic circuit that they have each considered quitting. However, Mitchell returned to the Middle East today for talks scheduled for to try tomorrow with Israeli and Palestinian leaders, trying to find a compromise that will open the way for peace talks.

Mitchell was appointed within days of Obama becoming president, a sign that the new administration saw the conflict as a priority. But it has proved slower and more frustrating than the administration had anticipated, with an Obama plan falling apart in September and talks deadlocked since then.

Mitchell's success in Northern Ireland, the result of patiently listening to both sides and winning their trust, does not guarantee him respect these days in Washington or the Middle East. He has already been criticised publicly by Israelis and Palestinians as a flop. And he has been criticised too in DC, against a background of infighting between advisers from the White House and state department over the way forward, one of the reasons that fuelled rumours he might quit. Mitchell faced criticism in the early days in Northern Ireland too, particularly from the Unionists, but painstakingly kept on going, just as he is doing in the Middle East.

On the Charlie Rose programme in January, he recounted a story about a lecture he delivered in Israel a year before his appointment, telling of his involvement in Northern Ireland. Asked afterwards by a member of the audience about the length of the Northern Ireland conflict, Mitchell confirmed it had been 800 years. His questioner replied: "No wonder you settled, it's such a recent argument." Mitchell went on to say on the programme that it would be naive for anyone to expect an early resolution.