While Mr Obama told the UN General Assembly there could be no place in Syria’s future for Bashar al-Assad, a “tyrant who drops barrel bombs on innocent children”, the Russian president urged the west to work with the “legitimate” Syrian government to defeat terrorism.

After the US president called for a “managed transition” towards a new leader in Syria, Mr Putin proposed the formation of a new international coalition to defeat the Islamist militants of Islamic State of Iraq and the Levant, known as Isis, that would be “similar to the anti-Hitler alliance” of the second world war.

The Russian leader said the Assad regime was crucial to the fight against Isis. “We think it is an enormous mistake to refuse co-operating with the Syrian government, which is valiantly fighting terrorism,” he said.

He also criticised the US-led coalition’s attempts to support opposition fighters in Syria. “The so-called moderate Syrian opposition supported by the west” could not be separated from terrorist groups as some of their fighters were deserting to join Isis, he said.

Spurred by the flood of refugees in Europe and the recent military build-up by Russia in Syria, the country’s civil war has become the main subject of this year’s annual meeting of leaders at the UN, which is celebrating its 70th anniversary.

Behind the scenes at the UN, diplomats have been working to try to restart negotiations about a political solution to the conflict, which has been stymied in the past in part through the very different perspectives of Washington and Moscow.

While the US believes Isis militants feed off anger at the Syrian government and that no viable solution to the conflict can include Mr Assad remaining in power, Russia argues the priority should be the defeat of Isis and that the Assad regime is an essential partner in that fight.

“Assad and his allies can’t simply pacify the broad majority of a population who have been brutalised by chemical weapons and indiscriminate bombing,” Mr Obama said. While compromise was required, Syria needed “a new leader and an inclusive government that recognises there must be an end to the chaos”.

Mr Obama said the US was willing to work with Russia and Iran to end the civil war in Syria, but that “after so much carnage” there could not be “a return to the prewar status quo”.

Mr Obama criticised Russia’s support for separatists fighting in eastern Ukraine, which he said was a violation of its sovereignty. “If that happens without consequence in Ukraine, it could happen to any nation gathered here today,” he said. In a speech that made a forceful case for democracy and international law, he warned that “the strong men of today become the spark of revolution tomorrow”.

Speaking after the meeting with Mr Putin, a senior administration official said that the two sides had a fundamental disagreement over the role of Mr Assad, with the Russians seeing him as a bulwark against extremism and the Americans viewing the Syrian leader as one of the main causes of the sectarian conflict.

The official said that the meeting had not been an exercise in “scoring points” and that there was “a shared desire to figure out a way in which we can address the situation in Syria”. But the official said the objective behind Russia’s military build-up was to both go after Isis and “support the government”.

The Russian leader used his speech to launch a broad attack on the “self-conceit and exceptionality” of US foreign policy since the end of the Cold War, which he said had brought instability to eastern Europe through the expansion of Nato and which stimulated Islamist terrorism by deposing leaders in Iraq and Libya.

“Do you realise now what you have done?” he asked, in reference to US-led interventions in the Middle East.

Iranian President Hassan Rouhani, whose government is another crucial supporter of the Assad regime, echoed Mr Putin’s theme by calling for a united international front to tackle terrorist groups in the region such as Isis.

“Iraq, Syria and Yemen are examples of how terror can create crisis,” Mr Rouhani said in his speech to the UN on Monday.

The senior US official said that the intelligence-sharing agreement between Russia and Iraq which was announced on Sunday was not significant because Moscow had little to offer Iraq.