This was a kind of direct intervention in Syria's six-year-old civil war his predecessor Barack Obama avoided.
The strikes were in reaction to what Washington says was a poison gas attack by the government of Syrian President Bashar al-Assad that killed at least 70 people in rebel-held territory. Syria denies it carried out the attack.
They catapulted Washington into confrontation with Russia, which has advisers on the ground aiding its close ally Assad.
"We strongly condemn the illegitimate actions by the US. The consequences of this for regional and international stability could be extremely serious," Russia's deputy UN envoy, Vladimir Safronkov, told a meeting of the UN Security Council on Friday.
Russian Prime Minister Dmitry Medvedev charged that the US strikes were one step away from clashing with Russia's military.
US officials informed Russian forces ahead of the missile strikes and avoided hitting Russian personnel.
Satellite imagery suggests the base houses Russian special forces and helicopters, part of the Kremlin's effort to help Assad fight Islamic State and other militant groups.
Trump has frequently urged improved relations with Russia, strained under Obama over Syria, Ukraine and other issues, was hosting Chinese President Xi Jinping at his Mar-a-Lago resort in Florida on Thursday night when the attack occurred.
Treasury Secretary Steve Mnuchin, in Florida with Trump, said on Friday the United States would announce additional sanctions on Syria in the near future but offered no specifics.
Russia's Defence Ministry responded to the attack by calling in the US military attache in Moscow to say that at midnight Moscow time (5 pm EDT) it would close down a communications line used to avoid accidental clashes between Russian and US forces in Syria, Interfax new agency said. US warplanes frequently attack ISIS terrorists in Syria and come close to Russian forces.
"Prepared To Do More"
US ambassador to the United Nations Nikki Haley said on Friday the Trump administration was ready to take further steps if needed.
"We are prepared to do more, but we hope that will not be necessary," she told the UN Security Council. "The United States will not stand by when chemical weapons are used. It is in our vital national security interest to prevent the spread and use of chemical weapons."
Secretary of State Rex Tillerson, who also was in Florida with Trump and is scheduled to go to Moscow next week, said he was disappointed but not surprised by the Russian reaction because it showed continued support for Assad.
The official also said the United States had been unable to determine if a Russian or Syrian aircraft bombed a hospital that was treating victims of the chemical attack.
Russia joined the war on Assad's behalf in 2015, turning the momentum in his favour. Although Moscow supports opposing sides in the war between Assad and rebels, the United States and Russia say they share a single main enemy, ISIS.
Tillerson said the strike took out about 20 per cent of the seventh wing of the Syrian air force and hit a fuelling facility. The base's runway was still in use.
Assad's office said Syria would strike its enemies harder.
Damascus and Moscow denied Syrian forces were behind the gas attack but Western countries dismissed their explanation that chemicals leaked from a rebel weapons depot after an air strike.
The Syrian army said the US attack killed six people and called it "blatant aggression" that made the United States a partner of "terrorist groups" including ISIS. There was no independent confirmation of civilian casualties.
Russia said the text was unacceptable and diplomats said it was unlikely to be put to a vote.
Moscow Wants Explanation
Russia expects Tillerson to explain Washington's stance when he visits Moscow next week, Interfax news agency cited a Russian Foreign Ministry spokeswoman as saying.
Washington has long backed rebels fighting Assad in a multi-sided civil war that has killed more than 400,000 people and driven half of Syrians from their homes since 2011.
The United States has conducted air strikes against Islamic State, which controls territory in eastern and northern Syria, and a small number of U.S. troops are helping rebel militias.
Asked whether the strikes set back any efforts to work with Russia to defeat Islamic State, sometimes known as ISIS, White House spokesman Sean Spicer said:
"There can be a shared commitment to defeat ISIS and also agree that you can't gas your own people."
Tuesday's attack was the first time since 2013 that Syria was accused of using sarin, a banned nerve agent it was meant to have given up under a Russian-brokered, UN-enforced deal that persuaded Obama to call off air strikes four years ago.
Video depicted limp bodies and children choking while rescuers tried to wash off the poison gas. Russian state television blamed rebels and did not show footage of victims.
The US strikes cheered Assad's enemies, after months when Western powers appeared to grow increasingly resigned to his staying in power. But opposition figures said an isolated assault was far from the decisive intervention they seek.
Neither the Trump administration nor its predecessor has laid out a policy aimed at ending the Syrian conflict.
(Additional reporting by Phil Stewart, Idrees Ali, Roberta Rampton and Patricia Zengerle in Washington, Steve Holland in Florida, Roselle Chen in New York and Denis Pinchuk in Moscow; Writing by Alistair Bell and Bill Trott; Editing by James Dalgleish and Lisa Shumaker)