Russian President Vladimir Putin has warned that further Western attacks on Syria would bring chaos to world affairs.
But there are signs that Moscow and Washington want to pull back from the worst crisis in their relations for years.
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Mr Putin made his remarks on Sunday in a telephone conversation with his Iranian counterpart Hassan Rouhani after the US, France and Britain launched missile strikes on Syria on Saturday over a suspected poison gas attack.
A Kremlin statement said Mr Putin and Mr Rouhani agreed that the Western strikes had damaged the chances of achieving a political resolution in the multi-sided, seven-year conflict that has killed at least half a million people.
"Vladimir Putin, in particular, stressed that if such actions committed in violation of the UN Charter continue, then it will inevitably lead to chaos in international relations," a Kremlin statement said.
The attacks struck at the heart of Syria's chemical weapons program, Washington said, in retaliation for a suspected poison gas attack a week ago. All three participants insisted the strikes were not aimed at toppling President Bashar al-Assad or intervening in the conflict.
The bombings, hailed by US President Donald Trump as a success but denounced by Damascus and its allies as an act of aggression, marked the biggest intervention by Western countries against Assad and ally Russia.
Mr Putin's comments were published shortly after Russian Deputy Foreign Minister Sergei Ryabkov struck a more conciliatory note by saying Moscow would make every effort to improve political relations with the West.
When asked whether Russia was prepared to work with the proposals of Western countries at the UN, Ryabkov told TASS news agency: "Now the political situation is extremely tense, the atmosphere is extremely electrified, so I will not make any predictions.
"We will work calmly, methodically and professionally, using all opportunities to remove the situation from its current extremely dangerous political peak."
Russian foreign ministry official Vladimir Ermakov said Washington would want to maintain a dialogue with Moscow about strategic stability after the raids, Russian media reported.
"In the US administration there are specific people who it is possible to talk with," said Mr Ermakov, head of the ministry's department for non-proliferation and arms control.
In Damascus, Syria's Deputy Foreign Minister Faisal Mekdad met inspectors from the global chemical weapons watchdog OPCW for about three hours in the presence of Russian officers and a senior Syrian security official.
The inspectors were due to attempt to visit the site of the suspected gas attack in Douma on April 7, which medical relief organisations say killed dozens of people. Moscow condemned the Western states for refusing to wait for OPCW's findings before attacking.
In an indication that the West, too, would prefer to lower tensions, the US and Britain both reiterated that their military action on Saturday was not aimed at Assad, Putin's ally, only at his use of chemical weapons.
Speaking to the BBC, Britain's Foreign Secretary Boris Johnson said that Western powers had no plans for further missile strikes, though they would assess their options if Damascus used chemical weapons again.
"This is not about regime change... This is not about trying to turn the tide of the conflict in Syria," he told the BBC, adding that Russia was the only country able to pressure Assad to negotiate an end to the conflict.
Asked about US-Russia relations, US ambassador to the United Nations Nikki Haley said ties were "very strained" but that the US still hoped for a better relationship.
Haley said the US would not pull its troops out of Syria until its goals were accomplished.
Russian Deputy Foreign Minister Sergei Ryabkov says Moscow would make every effort to improve political relations with the West, TASS news agency reports.
Ryabkov also said Russia would study a UN resolution on Syria proposed by the US, France and Britain, but added that it would be hard to reach a compromise on the issue, TASS reported.