US allies rallied around Washington after President Donald Trump launched the massive strike in retaliation for a "barbaric" chemical attack he blamed on Assad.
But Assad's office called the strike "foolish and irresponsible" and Moscow announced a series of retaliatory steps including plans to strengthen Syrian air defences.
Russia also demanded an emergency meeting of the UN Security Council and US diplomats said it was to meet at 11:30 am (local time) today.
It followed days of outrage at images of dead children and victims suffering convulsions from the suspected sarin gas attack in the rebel-held town of Khan Sheikhun.
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US officials said 59 Tomahawk cruise missiles were fired from Navy ships in the Mediterranean at the Shayrat airfield at 3:40 am (local time), dealing heavy damage to the base from where Washington believes Tuesday's deadly attack was launched.
Syrian state news agency SANA said nine civilians including four children were killed in villages near the base.
Syria's regime has denied using chemical weapons in Khan Sheikhun, where at least 86 people, including 30 children, were reported killed and more than 500 wounded.
With US Secretary of State Rex Tillerson due in Moscow next week, the Kremlin called the US strike a "gross... violation of international law" and warned it would inflict "considerable damage" on US-Russia ties.
It immediately suspended a deal with the United States aimed at avoiding clashes in Syrian airspace.
Foreign Minister Mohammad Javad Zarif of Iran, another staunch Assad ally, said on Twitter that the US strike was based on "bogus CW (chemical weapons) allegations" and would aid jihadists in Syria like the Islamic State group.
Britain, Canada, France, Germany, Israel, Japan, Saudi Arabia and Turkey all supported Washington, with Ankara also calling for a no-fly zone in Syria.
Trump announced the strike in a brief televised address delivered hours after the Security Council failed to agree on a probe into the suspected chemical attack.
The missiles were fired from the USS Porter and the USS Ross, which belong to the US Navy's Sixth Fleet, in the eastern Mediterranean.
The strike targeted radars, aircraft, air defence systems and other logistical components at the base south of Homs in central Syria.
In a statement read on state television, the army confirmed the strike and said it had caused extensive damage.
Russia's military said the strike had an "extremely low" military impact, with fewer than half of the 59 missiles reaching the base.
Opposition and rebel fighters, who have for years urged more direct US military action in support of their uprising, hailed the strike and called for more.
The National Coalition, the main opposition grouping, called on Washington to take further steps to "neutralise" the regime's air power.
"We hope for more strikes... And that these are just the beginning," spokesman Ahmad Ramadan told AFP.
Rebels have suffered a series of setbacks in recent years as Assad's forces have reclaimed much of the territory once under opposition control.
"I welcome this concrete step as positive," Erdogan said at a rally in the southern city of Antakya just north of the Syrian border. "I don't see this as enough... The time has come for steps for a serious result to protect the oppressed Syrian people."
But the White House was quick to paint the decision as limited to deterring the use of chemical weapons, and not part of a broader military campaign.
"The intent was to deter the regime from doing this again, and it is certainly our hope that this has had that effect," Pentagon spokesman Navy Captain Jeff Davis told reporters.
Russia stood by Damascus this week despite the global uproar, insisting that the chemical weapons that caused the deaths in Khan Sheikhun had been stockpiled by "terrorists" and possibly released by a conventional strike.
"We consider these strikes not only as a reaction, but a way to avenge the blood of the martyrs who fell here," said Haj Kassar, a merchant in his 50s.
Trump had previously indicated no willingness to engage further in Syria's civil war, beyond stepping up efforts to battle the jihadists of IS, who have been targeted by US-led air strikes in Syria and Iraq since mid-2014.
But Trump said the "very barbaric attack" in which "even beautiful babies were cruelly murdered" had required a response.