The US has given private assurances to encourage the Palestinians to join indirect Middle East peace talks, including an offer to consider allowing UN security council condemnation of any significant new Israeli settlement activity, the Guardian has learned.

The assurances were given verbally in a meeting a week ago between a senior US diplomat and the Palestinian president, Mahmoud Abbas. Since then – and after months of US diplomacy – it appears Israeli and Palestinian leaders are close to starting indirect "proximity" talks, which would be the first resumption of the Middle East peace process since Israel's war in Gaza began in late 2008.

There was no official confirmation of the details of the meeting and Saeb Erekat, the chief Palestinian negotiator, denied assurances were given. "It's not true," he said. "We are still talking to the Americans."

But a Palestinian source, who was given a detailed account of the meeting, said David Hale, the deputy of the US special envoy, George Mitchell, told Abbas that Barack Obama wanted to see the peace process move forward with the starting of indirect talks. The diplomat said Washington understood there were obstacles and described Israeli settlement construction as "provocative".

He told Abbas the Americans had received assurances from the Israeli prime minister, Binyamin Netanyahu, that one particular settlement project in East Jerusalem, at Ramat Shlomo, would not go ahead, at least for now. The site is important because last month an agreement on indirect talks collapsed within a day of being announced, after Israeli officials gave planning approval for 1,600 new homes in the settlement. The US vice‑president, Joe Biden, who was in Jerusalem at the time, condemned the Israeli announcement in unusually strong language.

Hale then told Abbas that if there was significantly provocative settlement activity, including in East Jerusalem, Washington may consider allowing the UN security council to censure Israel. It was understood that meant the US would abstain from voting on a resolution rather than use its veto.

Any US decision not to veto a resolution critical of Israel would be very unusual and a rare sign of American anger towards its long-time ally. However, it was not clear what may constitute significantly provocative activity. Palestinian officials asked in the meeting, but were not given an explicit definition, the source said.

In a New York Times opinion piece this week it was suggested that a letter was given to Abbas offering an unprecedented US commitment to the Palestinians and saying Washington would not stand in the way of a UN resolution condemning Israeli actions. But the Palestinian source told the Guardian that the assurances were only verbal and were not in letter form because the US wanted the details kept secret.

Erekat, the Palestinian negotiator, suggested they were close to agreeing to indirect talks. "We want to give President Obama a chance, to give Senator Mitchell a chance and of course success to us means independence and freedom," he said.

Last year, the Palestinians were refusing to enter talks without a full freeze on settlement building. Israel has put a partial, 10-month curb on construction in the West Bank, but Netanyahu has refused in public to freeze building in East Jerusalem. Last week he said Palestinian calls for a halt to settlement building in the city were an "unacceptable demand".

Yet reports suggest a tacit, temporary delay has been put on planning approvals for settlement projects in the city. Israeli ministers have said they believe the indirect talks could start within weeks and, privately, Israeli officials say there has been transparency with both sides about understandings reached to allow the process to begin.

Asked about Israeli settlement building, Erekat said: "I don't care about words. I care about deeds. I really want to see that nothing takes place on the ground. That is what matters to me."

Hani al-Masri, a political adviser to Abbas, said: "The Americans said they will blame the party that puts obstacles in the way of the peace process."

But he added that it was very unlikely that the Americans would allow the UN to censure Israel.

"We are very far from that step. They will never leave Israel to the mercy of the security council," said Masri.

US and Israel at the UN

For decades the US has vetoed UN security council resolutions that are critical of its ally Israel. However, occasionally the US either abstains from voting or votes in favour of sometimes strongly worded resolutions. This last happened in October 2000 when the US abstained in a vote over a resolution about the outbreak of the second intifada, the Palestinian uprising, which strongly criticised Israeli "provocation". The last time this happened regularly was between 1990 and 1992, when George Bush Sr was US president and when relations with Israel were particularly bad. His administration voted in favour of six resolutions critical of Israel