But Russia's ambassador to the US, Anatoly Antonov, warned of consequences after the strikes on its ally.
British Prime Minister Theresa May and French President Emmanuel Macron said the United Kingdom and France had joined in the attack.
According to a statement by the French presidency, Mr Macron called for dialogue between France and Russian Federation to "continue and intensify" to bring peace and stability to Syria.
Moscow also said it was calling an emergency session of the United Nations Security Council, where it is a permanent member, to discuss the "aggressive actions" of the U.S. and its allies.
US Ambassador Nikki Haley said the use of chemical weapons in Syria threatens world peace and that Russian Federation is responsible.
What is less clear is whether sarin - the agent used in the chemical attack last April that prompted United States missile strikes - or a similar agent was also used.
Trump warned on Wednesday that missiles "will be coming" in response to the Douma incident.
Vassily Nebenzia, Moscow's U.N. ambassador said he "cannot exclude" war between the United States and Russian Federation.
Chemical weapons experts for the Organisation for the Prohibition of Chemical Weapons (OPCW) arrived in Syria to investigate the suspected poison gas attack. Putin and Macron instructed their foreign and defence ministers to maintain close contact to "de-escalate the situation", the Kremlin said.
"God forbid anything adventurous will be done in Syria on the lines of the Libyan and Iraqi experience", he told a news conference, referring to Western interventions elsewhere in the region.
Karen Pierce said she wanted "to state categorically. that Britain has no involvement and would never have any involvement in the use of a chemical weapon".
The Kremlin on Saturday condemned Western air strikes on Syria where its armed forces are backing President Bashar al-Assad.
The capture of Douma from rebels who evacuated this week has clinched a major victory for Assad, crushing what was once a center of the insurgency near Damascus, and underlines his seemingly unassailable position in the war.
The Associated Press, citing a Russian media outlet, quoted a top Russian official as likening Trump to Nazi leader Adolf Hitler.
The Russian military says that an alleged chemical attack in Syria was staged and directed by Britain.
"Our President has not yet made a decision about possible action in Syria".
"We continue to observe risky military preparations for an illegal act of force against a sovereign state in what would constitute a breach of worldwide law", he said.
US allies have offered strong words of support for Washington but no clear military plans have yet emerged. A USA guided-missile destroyer, the USS Donald Cook, is in the Mediterranean.