Assad's allies rush to defend him despite chemical atrocity
General Valery Gerasimov and Major General Mohammad Bagheri spoke by phone and "condemned the American operation against a Syrian airbase which is an aggression against an independent country", Iran's state news agency IRNA said.
Russia and Iran are Syrian President Bashar al-Assad's closest allies, and label all opponents of his regime as "terrorists".
US warships in the Mediterranean launched a barrage of 59 cruise missiles at Shayrat airbase in Syria early on Friday, after 87 people including 31 children were killed in a suspected Syrian regime-sanctioned chemical attack on rebel-held Khan Sheikhun.
It was Washington's first direct military action against Assad's government.
Another Syrian regime or Russian airstrike on Saturday on the same town in the northwestern province of Idlib killed a woman, the Britain-based Syrian Observatory for Human Rights reported.
The monitor also reported an airstrike on Urum al-Joz, another Idlib town, on Saturday that killed 18 civilians including five children, which it said was believed to have been carried out by Russian aircraft.
Idlib province is controlled by a rebel alliance that includes a former al-Qaeda affiliate, and is regularly targeted by both the Syrian government and its Russian ally.
Russian Foreign Minister Sergei Lavrov accused Washington of "playing the terrorism game", during his first phone talks with his US counterpart Rex Tillerson since the US airstrikes on Syria.
Much of the international community accused Assad's government of carrying out Tuesday's suspected chemical attack on Khan Sheikhun, but Damascus denied responsibility.
|Read more: A timeline of Syrian regime chemical weapons attacks|
Pro-Assad camp reacts
North Korea denounced the US attack, calling it an "intolerable act of aggression" that "proves a million times over" that Pyongyang was right to strengthen its nuclear programme.
The statement by the Iranian and Russian military chiefs said they would continue their military cooperation in support of Assad "until the total defeat of the terrorists and those that support them", according to Iran's Mehr news agency.
The US strikes "aim at slowing the victories of the Syrian army and its allies, and reinforcing terrorist groups", they said in a statement.
Both Tehran and Moscow have defended Assad against Western allegations that his regime carried out the attack on Khan Sheikhoun.
As the Arab League on Saturday warned against a "dangerous escalation" in Syria, influential Iraqi Shiite cleric Moqtada Sadr called on Assad to step down and on Washington and Moscow to stop intervening in the conflict.
"I would consider it fair for President Bashar al-Assad to resign and leave power, allowing the dear people of Syria to avoid the scourge of war and terrorist oppression," he said.
Several Iraqi Shia militias, some of them directly supported by Iran, are helping Assad's camp by sending fighting units across the border.
The Syrian conflict began when the Baath regime, in power since 1963 and led by President Bashar al-Assad, responded with military force to peaceful protests demanding democratic reforms during the Arab Spring wave of uprisings, triggering an armed rebellion fuelled by mass defections from the Syrian army.
According to independent monitors, hundreds of thousands of civilians have been killed in the war, mostly by the regime and its powerful allies, and millions have been displaced both inside and outside of Syria.
The brutal tactics pursued mainly by the regime, which have included the use of chemical weapons, sieges, mass executions and torture against civilians have led to war crimes investigations.