The day before the strikes Russian President Vladimir Putin warned during phone talks with his French counterpart Emmanuel Macron against "ill-considered and unsafe actions" in Syria which could lead to "unpredictable consequences".
Putin called the military action a violation of the UN Charter and warned that if it continues, "it will inevitably entail chaos in global relations", according to the statement.
A Kremlin statement said Mr Putin and his Iranian counterpart, Hassan Rouhani, agreed during a telephone conversation that the air strikes had damaged the chances of achieving a political resolution of the conflict in Syria.
"Putin stressed that if such actions, committed in violation of the UN Charter, continue, it will inevitably lead to chaos in worldwide relations", RIA added.
Russia's Ministry of Defense claimed Syria's air defense systems intercepted 71 out of 105 missiles launched at three sites in Syria early Saturday morning local time in the airstrikes carried out by the United States, Great Britain and France in response to concern Assad's forces carried out a chemical attack against civilians in the rebel-held town of Douma last weekend that killed more than 70 people. I support tonight's worldwide military response, which demonstrates that there are consequences for using chemical weapons on innocent civilians.
The airstrikes received extreme backlash from Russian Federation, an ally of Assad's regime.
Kaine said the Syrian operations lack a clear strategy.
Francois Delattre, France's ambassador to the United Nations, said Syria's chemical weapons programme must be dismantled in a "verifiable and irreversible way".
The most expansive proposal, which might have included strikes on Russian air defenses in Syria, was created to cripple the regime's military capabilities without touching Mr. Assad's political machinery.
French President Emmanuel Macron said the country's objectives had been met and that no new strikes were planned at this point but promised to retaliate if the red line on chemical weapons was once again crossed.
Russian Federation vetoed a year ago the extension of the mandate of another joint U.N. -OPCW joint body in charge of determining who was behind chemical other weapons attacks in Syria.
Russian Federation and Iran condemned the strikes on Syria and vowed to stand by their ally - warning - there will be consequences.
Trump had said: "Mission accomplished" on Twitter after the strikes, although US Lieutenant General Kenneth McKenzie at the Pentagon acknowledged elements of the program remained and he could not guarantee that Syria would be unable to conduct a chemical attack in the future.
Mr Assad denies he has used chemical weapons, and the Trump administration has yet to present hard evidence of what it says precipitated the allied missiles attack - a chlorine gas attack on civilians in Douma on April 7.
The strikes have ratcheted up the worldwide tension, as the USA and Russian Federation exchanged threats of retaliation.
European Union foreign policy chief Federica Mogherini said the European Union wants to use a major meeting on Syria in Brussels next week to give impetus to United Nations peace efforts following the airstrikes.
On Saturday, the UN Security Council rejected a resolution drafted by Russian Federation, while all North Atlantic Treaty Organisation allies have given the military action their full support.