Syria's ally Russia says there should be talks between the Syrian government and the "full spectrum" of opposition.
Foreign Minister Sergei Lavrov also urged an intensification of efforts to find a political solution to the war.
Mr Peskov said the West had so far failed to identify any "balanced opposition" to Mr Assad that did not have links to jihadists.
Turkish Prime Minister Ahmet Davutoglu has confirmed that the Turkish military has attacked Kurdish fighters in northern Syria.
The Kurdish People's Protection Units (YPG) said Turkey shot at its forces in the town of Tal Abyad on Sunday.
The YPG has been a key ally of the US in fighting the so-called Islamic State (IS) group in Syria.
The Russian military has confirmed the death of one of its servicemen in Syria for the first time since it launched its campaign of air strikes last month.
The defence ministry in Moscow did not identify the soldier, who it said had committed suicide.
Family members identified him as Vadim Kostenko, 19, a soldier from the southern Krasnodar region, and disputed the official account of his death.
One official said it wasn't even a first step towards a peace process, just a tentative bid to seek common ground, with no-one really sure if that is possible.
Already the United States and its European and Arab allies, plus Turkey, have given some ground on the critical question of President Assad's role in any future process of transition, suggesting that although he would have to step down, it didn't have to be immediately.
Russia has reportedly sent missile systems to Syria to prevent possible hijacking of its jets
Totally strategic.
"If you try to hijack our planes, we'll shoot them down."
Its actually really strange. Putin doesn't need a reason to send weapons to Syria, so why pick a dumb one.
Meanwhile, Turkey has warned Russia that it must immediately stop bombing "civilian Turkmen villages" in Syria, close to the Turkish border.
The Russian ambassador to Ankara was summoned to the Turkish foreign ministry to hear the protest.
Turkey warned that bombing villages populated by the Turkmen minority could lead to "serious consequences".
It's creating an interesting dynamic. What happens when Russian/American/Turkish/Saudi etcetera fighters end up in the same airspace on different missions? It would take very little in the way of a miscalculation to see things go very bad very quickly.
Four Tornados from RAF Akrotiri in Cyprus took part in the operation soon after MPs voted to approve bombing.
The "successful" strikes hit the IS-controlled Omar oil fields in eastern Syria, the defence secretary said.
This morning's newspapers in Damascus reiterate criticism Syrian officials have made for years about the West's engagement here.
"Britain didn't ask permission from Syria's government," declares the state news agency SANA. "Cameron told lies," it says.
Syrian officials insist Britain and its allies must follow Russia's example and co-ordinate their campaign with Syrian government forces. If they don't, they warn, they simply won't succeed.
"The Syrian Arab Republic strongly condemns this flagrant aggression by the US-led coalition forces, which blatantly violates the objectives of the UN Charter," the foreign ministry warned.
The ministry called on the UN Security Council to "take urgent measures to prevent such aggressions from occurring again".
It added that such "aggression hinders the efforts to fight terrorism, and proves that the US-led coalition lacks seriousness and credibility to effectively fight terrorism".
However, coalition spokesman Col Steve Warren denied it was responsible.
"We've seen those Syrian reports but we did not conduct any strikes in that part of Deir al-Zour yesterday. So we see no evidence," he told the AFP news agency.
Few Russians hold their president directly responsible for the decisions he takes. That's partly because of the age-old tradition here of respecting the man at the top - the tsar, the emperor, the general secretary, whoever it may be. And, partly, because of Russian television which heaps praise on Vladimir Putin from morning till night.
...
"Vladimir Putin is a great ruler," the cadet tells me. "It's not just Russia that thinks so. But the whole world."
Homs was once dubbed the "capital of the revolution" and saw some of the first protests of the 2011 uprising.
But the truce means the entire city returns to government control, in a boost for President Bashar al-Assad.