MOSCOW (AFP) - Top US envoy John Kerry met Russia's President Vladimir Putin on Thursday (July 14) to offer him closer military cooperation in the hope of salvaging the stalled Syria peace process.

Ahead of the talks, pessimistic US officials were careful to say the trip was not a last chance for diplomacy to work, but stressed they were running out of patience with Moscow.

The key to the meeting, as revealed in a leaked document, is an offer for the US military to work with Russia against the Al-Nusra Front and Islamic State in Iraq and Syria (ISIS) militant groups.

In exchange, Russia would have to convince or strongarm its ally Bashar al-Assad into grounding his own planes and halting attacks on civilians and moderate opposition groups.

As the two sat down at the Kremlin they gave little away.

"I would like to note our mutual effort in the settlement of conflicts that we deem important to resolve," Putin said, conveying his regards to President Barack Obama.

"My last conversation with President Obama has convinced me that we are indeed striving not only to establish a process of cooperation but also to achieve important results."

Sitting across from him, Kerry, agreed that Obama had found the recent telephone call "constructive".

"Hopefully, we'll be able to make some genuine progress that is measurable and implementable and that can make a difference in the course of events in Syria," he said.

Kerry said Obama and he believed the US and Russia were in a position to make "an enormous difference" in the course of events not just in Syria but also in Ukraine.

But the diplomatic words could not conceal US concern and Washington said two major issues to be addressed were Assad's ceasefire violations and Al-Nusra's growing role.

"We need a solution to this that addresses both of these problems," a senior US official said.

"If we cannot get to a solution that resolves both of those problems we're going to be in a very different place, and the reality is that time is short here," he warned.

US officials downplayed the significance of the military offer, reported by The Washington Post, arguing they would have gone after Al-Nusra, an Al-Qaeda affiliate, anyway.

But critics of US policy are bound to see any offer to aid Putin's campaign in Syria - even against jihadists - as a victory for the Kremlin's intervention in Syria.

And there was no sign in Damascus that Assad feels under any pressure to agree to talks on a new government, the next stage in the process if a ceasefire is restored.

Speaking to NBC News in Damascus, Assad insisted Putin and Russian Foreign Minister Sergei Lavrov had never raised the issue of his departure or a political transition.

"Only the Syrian people define who's going to be the president, when to come, and when to go. They never said a single word regarding this," he said.

Moscow and Washington, and the 22-nation contact group they co-chair, have called for a nationwide ceasefire and Geneva-based talks on a "political transition".

A landmark partial ceasefire they brokered in February - which did not include ISIS or Al-Nusra - has since all but collapsed amid continued heavy fighting.

UN Syria envoy Staffan de Mistura urged Moscow and Washington to push for a resumption of the talks next month.

De Mistura said the talks "have a target date of August" and need to be "a credible beginning of a roadmap towards a political transition".

Russian forces are fighting in support of Assad's regime against a variety of rebel factions while a US-led coalition focuses its fire on the Islamic State group.

The Washington Post, citing a draft proposal from the United States, reported that the US and Russia could set up a joint command and control centre in Jordan.

This body would direct intensified air strikes against Al-Nusra, which is mainly fighting against Assad's forces.

In return, Moscow would limit its strikes to agreed targets and the Syrian air force would halt attacks in certain "designated areas." Syria's civil war erupted in 2011 when Assad brutally suppressed anti-government demonstrations and has evolved into catastrophe that has left more than 280,000 dead.

Efforts to bring an end to the war have taken on greater urgency since the emergence of ISIS, which seized control of large parts of Syria and neighbouring Iraq in mid-2014.