Syria's government on Saturday denounced the strikes on its military installations as a "brutal, barbaric aggression" that violated international law.
Its ally Russia accused the West of "fabricating" the chemical weapons incident to justify military action and said US President Donald Trump is taking America down a dangerous path.
Moscow's ambassador to the United States, Anatoly Antonov warned that such actions would not be left without consequences.
The Kremlin said in a statement that it wants to discuss "the aggressive actions of the US and its allies" at the UN Security Council, of which it is a permanent member.
The Russian military said Saturday that Western allies fired 103 cruise missiles, including Tomahawk missiles, at Syria but that Syrian air defence systems managed to intercept 71 of them.
Turkey was one of the first countries to approve of the Western strikes. Its foreign ministry said the reaction was an "appropriate response" in retaliation for a alleged chemical attack that left dozens dead on 7 April.
"We welcome this operation which has eased humanity's conscience in the face of the attack in Douma, largely suspected to have been carried out by the regime," the ministry said in a statement.
Turkey is a vocal critic of Assad's regime in Damascus and backed rebel forces but in recent months it has closely worked with Russia for a political solution in Syria even though Moscow remains Assad's chief ally.
European Council president Donald Tusk issued a statement saying the EU 'will stand with our allies' over Syria strikes, while Canada also issued a statement saying it supported the US decision to launch strikes.
British Prime Minister Theresa May said the operation was a "limited and targeted strike" but there was immediate criticism from opposition MPs who said May should have consulted parliament before joining US-led action in Syria.
Scottish First Minister Nicola Sturgeon said the strikes risked "dangerous escalation".
Vince Cable, leader of the Liberal Democrats, said: "Riding the coattails of an erratic US president is no substitute for a mandate from the House of Commons".
Other leaders have strongly condemned the Western intervention.
Israel declared that the strikes were an "important signal to the axis of evil - Iran, Syria and [Lebanese Shia-Muslim movement] Hezbollah".
“The use of chemical weapons crosses a red line that humanity can no longer tolerate,” Yoav Gallant, a member of Prime Minister Benjamin Netanyahu’s security cabinet, said on Twitter.
Officials said Israel was notified the attacks would take place several hours beforehand.
Iran's supreme leader Ayatollah Ali Khamenei condemned the strikes and warned of regional consequences.
"The attack this morning against Syria is a crime," Khamenei said in remarks published on his Telegram channel. "The American president, the French president and the British prime minister are criminals."
"The United States and its allies have no proof and, without even waiting for the Organisation for the Prohibition of Chemical Weapons to take a position, have carried out this military attack," an Iranian foreign ministry statement said.
Alongside Russia, Iran is Assad's key ally, providing military advisors and "volunteer" ground forces.
Lebanese movement Hezbollah, an ally of the Syrian regime, sharply condemned the strikes, saying they would not achieve their objectives.
"America's war against Syria, and against the region's peoples and resistance movement, will not achieve its aims," the group said in a statement published on its War Media Channel.