Top US diplomat John Kerry was to hold a second day of talks in Moscow on Friday in the hopes of salvaging the stalled Syria peace process.
Kerry held a first three hours of talks with President Vladimir Putin late Thursday and on Friday was due for a second round with Foreign Minister Sergei Lavrov.
Little filtered out about his Kremlin meeting with the Russian head of state, but Kerry's spokesman said he would "explore initiatives in more detail" with Lavrov.
According to a leaked document seen by the Washington Post, Kerry's key proposal is to offer Russia closer US military cooperation against the Al Nusra Front jihadist group.
In exchange, Moscow would be required to pressure its ally Syrian strongman Bashar al-Assad to ground his own jets and end attacks on civilians and the moderate opposition.
"The secretary expressed concern about repeated violations of the cessation of hostilities by the Syrian regime," State Department spokesman John Kirby told reporters.
"The two also discussed the need to need to increase pressure on terrorist groups like Daesh and the al-Qaeda affiliate in Syria, Jabhat al Nusra."
US officials were careful not to call the talks a last chance for diplomacy to resolve the bloody five-year-old conflict, but they warned time is running out.
Washington blames the failure of the peace process on Assad's ceasefire violations and on the Nusra Front's increasing influence among the surviving rebel factions.
"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," a US official said.
Meanwhile, 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.
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Speaking to NBC News in Damascus, in an interview broadcast Thursday, Assad insisted Putin and 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 IS 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 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 IS, which seized control of large parts of Syria and neighbouring Iraq in mid-2014.