Syria's opposition has dismissed assurances that President Bashar al-Assad is committed to ending the violence sweeping the country.
Mr Assad told visiting Russian Foreign Minister Sergei Lavrov he was prepared to co-operate with plans for stability.
Syrian government forces continued pounding the city of Homs on Wednesday morning, according to internet feeds and activist groups.
They claim more than 40 people have already been killed in the shelling.
The BBC's correspondent Jim Muir, in Beirut, says these figures must be treated with caution. They apparently include the deaths of 18 premature babies, who died after hospital electricity cuts meant their incubators failed, he says.
Three families in Homs were killed by pro-government thugs who burst into their house and slaughtered them, reports say.
The US said it was not sure what the purpose of the Russian foreign minister's visit was.
Following the talks in Damascus on Tuesday, Mr Lavrov called for a dialogue between the Syrian government and opposition.
"We have every reason to believe that the signal that we've brought here to move along in a more active manner along all directions has been heard," he said.
"In particular, President Assad assured [us] that he is fully committed to the task of a cessation of violence, from whatever source it comes."
Mr Lavrov called for a solution based on an Arab League initiative from last November, but gave no indication that Russia backed the league's more recent call for Mr Assad to step down.
The official Syrian news agency Sana later quoted Mr Assad as saying he "welcomed any efforts toward a solution to the crisis".
But opposition leaders said continuing bloodshed meant it was too late for Mr Assad to offer compromises.
"It is impossible for Assad to govern after bombarding his own cities and towns," opposition leader-in-exile Kamal al-Labwani told Reuters.
"He is escalating the use of his military might either to sink Syria into chaos or to improve his negotiating position."
White House spokesman Jay Carney said the US was not sure what the goals of Mr Lavrov's visit to Damascus had been.
"Russia must realise that betting everything on Assad is a recipe for failure, not just for Russia's interests in Syria but for the stability of the region and for Syria's future," he said.
Last week Russia and China vetoed a UN resolution that backed a new Arab League plan for Syria. The plan involved Mr Assad handing power to a deputy who would oversee a transition of power.
Moscow said the draft would have forced regime change on Syria.
Since then, Syria has become increasingly isolated.
On Tuesday, Gulf Arab states said they would expel Syrian ambassadors and recall their envoys from Damascus.
The US closed its embassy in Syria on Monday, and several European countries have recalled their ambassadors.
In Homs, hundreds of people are reported to have died in days of heavy shelling. At least 95 people were killed on Monday and another 15 on Tuesday, activists say.
The government insists it is confronting "terrorist groups" in the city and will continue until "order" is restored.
Continuing violence against protesters has also been reported in other parts of Syria.
Activists said tanks bombarded the town of Zabadani, about 30kms (19 miles) north-west of Damascus, on Tuesday.
Witnesses also reported clashes between government and rebel forces in Hama, another stronghold of anti-Assad sentiment.
Syria heavily restricts access to foreign journalists and the reports cannot be independently verified.
Human rights groups and activists say more than 7,000 people have been killed by Syrian security forces since the uprising began last March.
The UN stopped estimating the death toll in Syria after it passed 5,400 in January, saying it was too difficult to confirm.
President Assad's government says at least 2,000 members of the security forces have been killed.