The US special envoy to the Middle East, George Mitchell, is due to fly to the region on Sunday to try to secure a resumption of Israeli-Palestinian talks amid optimism about a breakthrough.

Mitchell had been due to visit Israel on Tuesday but his trip was cancelled – a victim of US-Israeli tensions. It was reinstated after Israel's prime minister, Binyamin Netanyahu, bowing to US pressure, phoned the secretary of state, Hillary Clinton, last night to offer concessions.Mitchell is scheduled to see Netanyahu in Israel and the Palestinian leader, Mahmoud Abbas, in Ramallah.

Tony Blair, envoy of the Middle East Quartet group of the US, the UN, the EU and Russia, predicted talks between Israel and the Palestinians could start soon. Blair, who was in Moscow today, told Reuters he expected proximity talks, indirect negotiations between the Israelis and Palestinians, with the US as a broker.

"I hope very much that in the next few days we will have a package that gives people the sense that, yes, despite all the difficulties of the past few days, it is worth having proximity talks and then those leading to direct negotiations," he said.

The Quartet issued a statement reiterating its hope that the talks would lead to a settlement within 24 months and condemning the plan to build 1,600 Jewish homes at Ramat Shlomo in East Jerusalem.US-Israeli relations deteriorated quickly after Israel's surprise announcement last week about the homes.

Clinton phoned Netanyahu and set out demands including confidence-building measures that could include withdrawing roadblocks on the West Bank, releasing Palestinian prisoners, and removing soldiers from parts of the West Bank. She also demanded a freeze on new Jewish settlements on Palestinian territory such as that planned for Ramat Shlomo.

Today she told a press conference in Moscow, where she had been at the Quartet group meeting: "What I heard from the prime minister in response to the requests we made was useful and productive and we are continuing our discussions with him and his government."

Netanyahu's office and the US state department would only say publicly that he had agreed to confidence-building measures, and made no reference to a moratorium on settlements. But diplomats and analysts said that there would also have been private undertakings for such a moratorium, sufficient to allow the Palestinians to agree to resume talks.

Clinton, in a BBC interview, suggested the pressure on Netanyahu was bringing results: "I think we're going to see the resumption of the negotiation track, and that means that it is paying off."

She will try to get Netanyahu to commit himself to specific details when the two meet next week in Washington. The White House today declined to confirm whether Barack Obama would meet Netanyahu too.

Daniel Levy, a former Israeli government peace negotiator and now an analyst based in Washington, said he believed Netanyahu would have promised Clinton not to undermine US peace efforts with any more surprise announcements of settlement building. "I think there will almost certainly have been private undertakings by Bibi [Netanyahu] to adhere more rigorously to the embarrassment test, meaning no settlement announcements or developments, evictions or demolitions in both Jerusalem and the West Bank," Levy said.

Hussein Ibish, a senior fellow at Washington's American Task Force on Palestine, thought Netanyahu would have given enough ground to allow the Palestinians back into the talks. "The Obama administration has made its point and extracted pretty significant assurances," Ibish said. "I think it will be enough for the Palestinians to go into the proximity talks. Netanyahu tried to defy Obama and did not get away with it."

Aaron David Miller, an adviser to six secretaries of state on Middle East negotiations, said the call between Clinton and Netanyahu was "an effort to walk the cat back from the heat and fire of the last week". He expected a resumption of indirect talks but was pessimistic about the chances of peace in the long term. "It is hard to see a way to an outcome. They could agree on borders but not Jerusalem and refugees … the gaps are too long for this Israeli government and I suspect too for the Palestinians," he said.

David Makovsky, director of the Washington Institute for the Near East Project on the Middle East Peace Process, said the peak of the crisis was "clearly behind us". But he suggested there could be more drama on Monday when Clinton is due to address the Israeli lobby group Aipac in Washington. "When you get a crowd of 7,500 people, it is hard to predict that all 7,500 will behave appropriately. The organisation is trying to make it clear she should be received respectfully. The question is whether they can get 100% compliance," Makovsky said.

Meanwhile, Hamas security officials and witnesses said Israeli aircraft struck at targets in the Gaza Strip yesterday, a day after a rocket from the Palestinian enclave killed a Thai worker in Israel. Eleven people were wounded in Israeli strikes, which targeted smuggling tunnels along the border with Egypt, a foundry near Gaza City and the non-operating airport.