A frustrated US Secretary of State John Kerry is heading back to Moscow once again to meet President Vladimir Putin and test his commitment to the stalled Syrian peace process.

Russia and the United States are nominally co-chairs of international efforts to bring Bashar al-Assad's regime to the negotiating table with armed opposition groups.

But ferocious bloodshed continues in defiance of a series of failed ceasefires, and the odd couple heading the peace effort appear increasingly at odds over the way forward.

Kerry told diners at a delayed Eid al-Fitr supper Tuesday that he would meet Putin "to see if we can somehow advance this in the important ways that people want us to."

And he told the State Department guests: "You have my word -- all of you -- that we will continue doing everything that we can to alleviate the suffering in Syria."

But, as Kerry's spokesman John Kirby said of his boss to reporters earlier: "I'd say he's extremely frustrated, and we want to see real change in what's been going on.

"I believe he meant every molecule of what he said when he said that his patience was growing thin," Kirby said.

In Washington, many observers have criticized Kerry's outreach to Russia on Syria, arguing he has been strung along by a Putin seeking only to protect his client Assad.

But Kirby insisted the administration is not being naive, and that Thursday's visit to Moscow, Kerry's third this year, would "probe the sincerity" of Putin's promises.

Hopes for the existing peace process rest on the UN-backed blueprint sketched out by the 22-nation, US and Russian-led International Syria Support Group (ISSG).

- Drop dead date -

Under this road map, signed by both Syria's ally Iran and Assad's pro-rebel foe Saudi Arabia, a nationwide ceasefire will precede Geneva-based talks on "political transition."

Substantial political talks were once supposed to start on August 1, although Kerry has sought to underline that this is a "target" and not a "drop dead date" nor deadline.

Before leaving on Wednesday with Kerry for Paris, from where he was due to fly on to Moscow, the spokesman said "we're mindful of the clock. We're mindful of the calendar."

Kirby said talk of the August 1 target date "underscores the importance of the secretary's trip to Moscow and the conversations that he intends to have there."

But he added "clearly, we are not ignorant to the fact that achieving some sort of groundbreaking political development in two weeks is not likely."

Previously, Kerry has suggested that if there is no breakthrough by the target date then Washington might resort to an undefined "Plan B" to deal with Assad.

- Open to ideas -

He and other US officials have since played down this idea -- reportedly a call for military strikes against the regime -- but it is not clear if they have other options.

There have been suggestions that the US and Russia might coordinate their forces to jointly go after the jihadists of the Al-Nusra Front and the so-called Islamic State.

On this, Kirby said the US was "open to ideas."

But on the civil war itself, Washington and Moscow are still far apart, and Kerry's counterpart Foreign Minister Sergei Lavrov places the blame on the United Nations.

Lavrov said on Tuesday that UN envoy Staffan de Mistura was "shunning his duties" in not summoning the warring parties to a new round of peace talks in Geneva.

On Monday, De Mistura said he wants guarantees of progress before restarting the process, warning "the key lies in a possible agreement between Russia and the United States."

Washington defends De Mistura, arguing it is hard to expect the moderate opposition to come to the table while Russian-backed Syrian forces are bombarding them daily.

"Russia can play a more productive, more constructive, more useful role in terms of trying to check that behavior," Kirby argued, citing Assad's forced starvation tactics.

"And so we'll see where we get after the discussions... and we'll see where we get throughout the rest of July."