David Cameron is in the United States and has appeared on CBS television saying that President Putin needs to realise that there will not be stability in Syria unless Bashar al-Assad is removed from power.
The prime minister said the only way to have a Syria free of Islamic State is to have a country free of President Assad.
Barack Obama and Vladimir Putin discussed the possibility of Russian involvement in the military campaign against the so-called Islamic State (IS) during their meeting on Monday.
Both sides agreed to direct their militaries to hold talks to avoid conflict over potential operations in Syria, according to a US official.
The Agence France-Presse news agency quoted Putin as saying that Russia had not ruled out taking part in air strikes with the US-led coalition against IS, but would not be sending in ground troops.
We are thinking about it. We don't rule anything out. But if we are to act it will only be fully respecting international legal norms.
President Obama emphasised that the United States would work with Russia and Iran to find a solution to the bloodshed in Syria, although he differed with President Putin over working with Syria's President Bashar al-Assad.
Qatar's foreign minister has said he believes the first priority in Syria should be to fight President Bashar al-Assad.
Referring to the disagreement between Russia and the US over the fate of Syrian president Bashar al-Assad, Khaled al-Attiyah said: "Nobody can reject Mr [Vladimir] Putin's call for an alliance against terrorism, but ... we need to treat the cause.
"We believe strongly that the Syrian regime, namely Bashar al-Assad, is the real cause."
Barack Obama and Vladimir Putin have agreed to explore a political solution to Syria's conflict, but continue to disagree on the future of Syrian President Bashar al-Assad, according to a US official.
During the two leaders' 90-minute meeting on the sidelines of the UN summit, Mr Obama told Mr Putin that he saw no path to stability in Syria if Assad remains in power, according to the official.
The two leaders spent about half their meeting discussing Syria, and half discussing Ukraine, Mr Obama said.
Mr Putin said the meeting was "very useful and frank".
There were frosty relations between Barack Obama and Vladimir Putin as they met at a UN Summit to discuss Syria.
The US President said he thought Syrian President Bashar al-Assad was a "tyrant" who was behind the four-year civil war in which at least 200,000 people have died.
While Russian premier Putin told the gathering of world leaders there was no alternative to cooperating with Assad's military to defeat the so-called Islamic State.
The pair shook hands and clinked glasses at a lunch hosted by UN Secretary-General Ban Ki-moon.
Fifty countries have pledged over 30,000 new troops and police for possible deployment on United Nations peacekeeping missions, US president Barack Obama has said.
More than 50 countries, from Bangladesh to Colombia, from Finland to China, are making commitments totaling more than 30,000 new troops and police.
Mr Obama was speaking at a summit of world leaders organised by the US to boost global support for UN peacekeeping missions.
The Syrian crisis has dominated the agenda throughout the meetings in New York.
Barack Obama has said he is prepared to work with Russia and Iran and any other world leaders to bring an end to the Syria crisis.
Addressing the UN General Assembly, the US President said there can be no return to the status quo in Syria under "tyrant" President Bashar al-Assad.
However Russian president Vladamir Putin later told the Assembly it was an "enormous mistake" to refuse to work with Assad's government and its armed forces.
ITV News Washington Correspondent Robert Moore reports:
Russian president Vladamir Putin has said it is an "enormous mistake" to refuse to work with the Syrian government.
Addressing the UN General Assembly, Putin said: "We think it is an enormous mistake to refuse to cooperate with the Syrian government and its armed forces who are valiantly fighting terrorism face to face.
"We should finally acknowledge that no one but President Assad's armed forces and (Kurdish) militia are truly fighting the Islamic State and other terrorist organizations in Syria."
He called for the creation of a broader international anti-terrorist coalition including Muslim states as key members.
There can be no return to the status quo in Syria under 'tyrant' President Bashar al-Assad, Barack Obama told the UN Assembly.Read the full story ›