The new pressure on Assad came as Moscow revved up its bid to save a tattered peace process by first hosting a top Damascus envoy and then planning for a meeting Saturday with Syria peace mediator Lakhdar Brahimi.
Russia also invited the head of the opposition National Coalition for talks in either Moscow or a regional capital -- the Kremlin's first contact with a group formed in November and recognised by the West as the legitimate representative of all Syrians.
But Moscow still views Assad as the legitimate leader, and its outreach to the regime's opponents found a cool response from the National Coalition chief.
Ahmed Moaz al-Khatib told Al Jazeera television that he would meet the Russians outside Moscow only under the condition that they issued "a clear condemnation of the crimes committed by the Syrian regime."
The fast-paced but tricky diplomacy came against the backdrop of air raids by Syrian warplanes on a Damascus province from which Assad's forces had to withdraw the night before.
"The air force for the first time attacked the Assal al-Ward area in the Kalamun region, killing one civilian, wounding dozens and destroying several homes," the Britain-based Syrian Observatory for Human Rights watchdog said.
Russia's Foreign Minister Sergei Lavrov said Moscow still refused to back international calls on Assad to step down and expected the Syrian people to decide their own country's fate.
'Change should not be cosmetic'
But he made explicit that Russia wanted Assad to put all options on the table after 21 months of violence that has claimed more than 45,000 lives.
"We actively encouraged... the Syrian leadership to maximally put into action its declared readiness for dialogue with the opposition," Lavrov told reporters when asked about his meeting Thursday with Syria's Deputy Foreign Minister Faisal Muqdad.
He noted that Russia hoped to see Assad's government "underscore that they are open to discussing the widest range of items in line with the agreements reached in Geneva on June 30."
That accord -- rejected by the opposition and never implemented because of the fighting -- sought to quickly establish an interim coalition government but made no direct call on Assad to step down.
Western and Arab nations have chastised Russia for continuing to supply Damascus with weapons and refusing to accept that no solution was possible with the regime still in power.
Yet the West lacks direct access to Assad and needs Russia to put across the message to the regime that its days are numbered and that it cannot hang on to power through force alone.
Moscow has in the last weeks moved to distance itself from the rulers of what was its last big ally in the Middle East.
President Vladimir Putin has twice this month said that Moscow had no intention of propping up Assad, and Lavrov himself warned Thursday that time was running out for Damascus to accept the terms of the Geneva accord.
Lavrov's warning came in the context of continuing gains by the armed opposition and an earlier admission by Moscow that Assad's forces may not hold out for much longer.
"Russia has long realised that Assad has no future," said Carnegie Moscow Center analyst Alexei Malashenko.
Efforts to revive diplomacy will continue in Moscow on Saturday following Brahimi's extended visit to Damascus for talks with both Assad and opposition heads.
The Algerian diplomat revealed Thursday that he had been discussing the details of a transition government that had full powers and implemented "real change".
"Change should not be cosmetic; the Syrian people need and require real change, and everyone understands what that means," Brahimi said on the fifth and final day of his stay in Damascus.
Yet Lavrov stressed Friday that all peace efforts were futile unless the West impressed on the armed opposition the need to engage in talks that left open the possibility for Assad to stay on an interim basis.
"I hope that the situation inside Syria will prompt reasonable members of the opposition to search for a way to start a political dialogue," Lavrov said.