US President Barack Obama and Russian President Vladimir Putin agreed on the need for a diplomatic solution to the Syrian civil war but found themselves on opposite poles on the fundamental question of whether Syrian President Bashar al-Assad should retain power.

The two world leaders talked for over 90 minutes on the sidelines of the UN General Assembly on Monday, a CNN report said.

Obama and Putin agreed that their armed forces should hold talks to avoid a dangerous confrontation in Syria as Moscow continued deploying air and ground forces in the war-torn Middle East country.

Obama reportedly asserted that Assad must step down because Syria will never be stable as long as he stays in power.

He described Assad as the "chief culprit" that caused the deaths of least 200,000 people and the displacement of millions as a result of the four-year civil war in Syria.

But Putin countered that the Syrian leader is the only alternative to cooperating with government troops in fighting against the Islamic State and other Islamic extremist groups in the region.

He also called for the creation of an international anti-terrorist coalition broader than the coalition the US has assembled to fight the ISIS.

In his address to the UN General Assembly, Obama told the world body that "the United States is prepared to work with any nation, including Russia and Iran, to resolve the conflict... But we must recognise that there cannot be, after so much bloodshed, so much carnage, a return to the pre-war status quo."

After Obama's address, the Russian leader followed in the rostrum, saying that "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 organisations in Syria,'' Putin said.

Aside from Obama, French President Francois Hollande and Turkish Prime Minister Ahmet Davutoglu also rejected the possibility of allowing Assad to stay in power.

But both leaders, however, affirmed the need for a political resolution. They agreed that their armed forces should hold talks to prevent unintended clashes. US troops are said to be carrying out airstrikes in that country while Russia is reportedly beefing up support for Assad's troops.

On Wednesday, Russia commenced its airstrikes on Syrian enemy targets.

The United States, France and allied countries are also carrying out a bombing campaign against ISIS militants, who have exploited power vacuums in the region to seize parts of Syria and neighbouring Iraq as part of their stated goal of creating an Islamic caliphate, Newsmax said.

Donald Trump: 'Let Russia get rid of ISIS'

Meanwhile, Republican presidential hopeful Donald Trump said the US strategy against ISIS in Syria should be changed by letting Russia take the lead, noting that Moscow is allied with the Assad regime.

"Russia wants to get rid of ISIS. We want to get rid of ISIS. Maybe let Russia do it. Let them get rid of ISIS. What the hell do we care?'' Trump said in a "60 Minutes'' interview that aired Sunday on CBS.

But the GOP front-runner said that in Iraq, he would be willing to send ground forces to fight the radical militant group.