It was the first time the United States has intervened directly in the Syrian civil war against the Russian-backed regime of President Bashar al-Assad.
USA officials have said the Pentagon is looking for any evidence the Russian government knew about or was complicit in Tuesday's chemical attack.
British Foreign Secretary Boris Johnson, meanwhile, canceled his planned Monday visit to Moscow, citing developments in Syria.
The move immediately prompted a backlash from Russian President Vladimir Putin, who said it would damage U.S.
"My priority is now to continue contact with the US and others in the run up to the G7 meeting on 10-11 April", said Johnson, who was due to travel to Moscow on Monday, lamenting "Russia's continuing defence of the Assad regime".
But for the most part, the Russia-backed Syria regime has left the United States coalition to conduct operations as the two sides focus on different foes in the tangled conflict. But in the aftermath of the attack, Trump ordered the strike targeting the Shayrat air base in central Syria's Homs province with 59 Tomahawk missiles.
Russian Sen. Alexey Pushkov said the disappointment was mutual and suggested Tillerson's comments were made to gain leverage in upcoming US-Russia talks.
So far, the Russian military does not appear to have taken any threatening actions, such as directing its battlefield radar or air defense systems to confront the Americans, or carrying out aggressive actions in the skies, USA officials said.
"We don't believe we need dialogue with London more than (London) needs it (with us)".
Pence to North Korea: 'The sword stands ready'
China recognizes that North Korea is a problem, but it is pursuing a distinctly different path to a resolution than the U.S. After referencing Pence's trip, Earhardt asked Trump whether he has ruled out a military strike against North Korea.
The US strike against Syria was strongly condemned by Russian Federation, which also threatened to cut cooperation with the Americans in the fight against terror in Syria.
"Those attacks did not reduce the regime's ability kill civilians".
He declined to say whether Trump now believed Assad should relinquish power.
In Florida with the president, Treasury Secretary Steven Mnuchin said additional economic sanctions on Syria were being prepared. After months of allegations of ties between his election campaign and the Kremlin - the subject of current congressional and FBI investigations - Trump has found himself clashing with Putin. Shortly afterward, officials say the hospital was targeted.
On Friday, senior US military officials were looking more closely at possible Russian involvement in the poison attack. Spokesman Sean Spicer said the missile attack sent a clear message to Assad, but he avoided explicitly calling for the Syrian to leave office.
The White House refused to discuss next steps.
Although Syria itself is not a major oil producer, especially in the last few years while the civil war has been raging, it neighbors Iraq; any increase in tension within Syria is likely to reverberate across the Middle East and beyond, especially now that the latest events have put the US and Russian Federation at odds.
The army chiefs of Assad's closest allies ─ Russian and Iranian ─ vowed Saturday to keep battling "terrorists" in Syria.
Iranian President Hassan Rouhani has called for the formation of an worldwide fact-finding committee to investigate the attack and make clear where the chemical weapons came from.
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