The Palestinian leadership remains prepared to put statehood on the backburner at the UN security council in order to leave room for the revival of peace talks, according to senior Palestinian sources.

The Palestinian leader, Mahmoud Abbas, is said to have told Barack Obama at a meeting on Wednesday evening that he would agree to delaying a security council vote by several weeks, although the Palestinians are maintaining the line in public that any delays will be "procedural not political".

The Palestinian offer comes despite Obama angering them by defending the US threat to veto the bid for statehood while praising revolutions in other parts of the Arab world.

Obama told the opening of the UN general assembly in New York that negotiation between Israel and the Palestinians, not a security council resolution, was the way to ensure a lasting peace. But he was challenged by the French president, Nicolas Sarkozy, who said US leadership on the issue had failed and called for a new initiative involving Europe and Arab states to create a Palestinian state within a year.

Sarkozy's intervention fits with a plan being mapped out by the Quartet of the UN, US, EU and Russia to restart negotiations and avoid a showdown in the security council. The French president said there should be talks without preconditions. But the Quartet plan faces a major obstacle from a Palestinian insistence that it require Israel to halt all settlement construction during talks.

Obama said "the Palestinian people deserve a state of their own" and that vision had been delayed for too long. But he offered no new initiatives and, tellingly, did not repeat earlier calls – for which he has come under fire – for negotiations to be based on the borders at the time of the 1967 war, with agreed land swaps. He also made no mention of settlements.

Obama went from his speech to a meeting with the Israeli prime minister, Binyamin Netanyahu. The US president was dismissive of Abbas's plan to ask the security council to recognise Palestine as a state.

"Peace will not come through statements and resolutions at the UN – if it were that easy it would have been accomplished by now. Ultimately it is Israelis and Palestinians who must live side by side. Ultimately it is Israelis and Palestinians – not us – who must reach agreement on the issues that divide them: on borders and security, on refugees and Jerusalem," he said as Abbas shook his head.

The Palestinians responded by saying they would not be deterred from pursuing their request to the security council for full membership of the UN, and that if he US used its veto they would seek a vote in the general assembly, which has the power to grant observer status.

However, the Palestinians appeared to be pulling back from an immediate confrontation, having come under intense pressure from the Europeans as well as the Americans. Although Sarkozy staked out a position sympathetic to the Palestinian cause in his UN speech, he has advised Abbas to hold off from the security council move.

Another senior Palestinian official, Nabil Shaath, said the Palestinians had an assurance from the UN secretary general, Ban Ki-moon, that a vote in the security council would not be delayed for political reasons, but only by procedure. He said that if there was no request for the vote, or the US exercised its veto, then the Palestinians would go to the general assembly. But he declined to put a timescale on such a move.

In a speech that was widely seen as his most supportive of Israel as president, Obama spoke about the US's "unshakeable" commitment to the Jewish state's security, and said that any lasting peace must recognise Israel's "very real security concerns". He spoke at length about Israeli suffering, but to the consternation of the Palestinians made no mention of the difficulties of life under occupation or the impact of expanding Jewish settlements in the West Bank and East Jerusalem.

Obama said: "Let's be honest: Israel is surrounded by neighbours that have waged repeated wars against it. Israel's citizens have been killed by rockets fired at their houses and suicide bombs on their buses. Israel's children come of age knowing that throughout the region, other children are taught to hate them.

"Israel, a small country of less than 8 million people, looks out at a world where leaders of much larger nations threaten to wipe it off of the map. The Jewish people carry the burden of centuries of exile, persecution and the fresh memory of knowing that six million people were killed simply because of who they were.

"Friends of the Palestinians do them no favours by ignoring this truth, just as friends of Israel must recognise the need to pursue a two-state solution with a secure Israel next to an independent Palestine."

Obama's failure to offer any new hope of progress toward a Palestinian state stood in sharp contrast to his praise of the quest for freedom in parts of the Arab world and beyond. "Something is happening in our world. The way things have been is not the way they will be. The humiliating grip of corruption and tyranny is being pried open," he said.

Sarkozy said the "miracle" of the Arab spring was a reminder of the moral and political obligation to resolve the Israeli-Palestinian conflict. But without naming the US, he implied that its oversight of years of failed negotiations meant a new approach was required. "We can wait no longer. The method is no longer working? Change the method. Cease believing that a single country or a small group of countries can solve a problem of such complexity."

Sarkozy called for a fresh set of negotiations, with wider involvement of European and Arab nations, based on a timetable that would see the borders of a Palestinian state agreed within six months and a final deal within a year. "We should not look for the perfect solution. Choose the path of compromise," he said.

But Sarkozy also said the Palestinians were mistaken to seek full recognition as a state at the security council. He warned there could be violence if the bid went ahead and was vetoed by the US. The French president said the Palestinians should instead ask to be admitted as an observer state to the general assembly, which would give them hope.

Shaath criticised Obama's speech for failing to address what he said was the primary obstacle to peace negotiations: the continued construction of Jewish settlements in the occupied territories. "The serious gap in the speech had to do with the absolute minimum for the peace process ... settlement policies, de-Arabisation of Jerusalem, the siege of Gaza," he said.

Hanan Ashrawi, the Palestinian former negotiator who is part of Abbas's delegation to the UN, told the Israeli newspaper Haaretz she was angered by Obama's speech.

"I did not believe what I heard, it sounded as if the Palestinians were occupying Israel. There was no empathy for the Palestinians, he only spoke of the Israeli problems," she said. "He told us that it isn't easy to achieve peace – thanks, we know this. He spoke about universal rights – good, those same rights apply to Palestinians.

"[The Americans] are applying enormous pressure on everybody at the UN, they are using threats and coercion. I wish they would invest the same energy in an attempt to promote peace, not threats."

Obama's speech was greeted with despair in the West Bank. Mustafa Barghouti, an independent politician and former Palestinian presidential candidate, said he was disappointed. "It clearly shows the double standards of the US when it comes to the Palestinian issue. Obama spoke about freedom, human rights, justice in South Sudan, Tunisia, Egypt – but not for the Palestinians," he said.

"His version of reality is wrong. He claims that Israel is the victim in this conflict and that's not true. He doesn't see that this is not a struggle between two equal sides, but between an oppressor and the oppressed, and occupier and the occupied."

A Ramallah shop owner, Marwan Jubeh, said: "Israel and the US are one and the same: the US is Israel, and Israel is the US. Israel doesn't want to give the Palestinians anything and Obama can't do anything without Israel because Congress is pro-Israel."

In contrast, Netanyahu praised Obama when the two met after the US president's speech. The Israeli prime minister described Obama's pledge to block the Palestinian move at the UN security council as a "badge of honour".

Netanyahu said he was ready for talks with the Palestinians but was sceptical about what they could achieve. "I think the Palestinians want to achieve a state but they're not prepared yet to make peace with Israel," he said.