The UK says it "fully supports" the US missile strike in Syria and has urged Russia to put more pressure on the Assad regime to end the civil war.
The US targeted an air base it says was responsible for a chemical attack which killed dozens of civilians.
Defence Secretary Michael Fallon said the UK was not asked to take part but backed the "wholly appropriate" strike.
But Labour Leader Jeremy Corbyn said the US action "risks escalating the war in Syria still further".
The opposition leader's words put him at odds with Labour's deputy leader Tom Watson and former shadow foreign secretary Hillary Benn, who have backed the US action.
Fifty-nine Tomahawk cruise missiles were fired from two US Navy ships in the Mediterranean. Six people were killed, the Syrian army said.
The strike comes days after dozens of civilians, including children, died in a suspected nerve gas attack on the rebel-held town of Khan Sheikhoun in north-western Syria.
The Kremlin, which backs Bashar al-Assad, has condemned the action as an "act of aggression under a completely invented pretext ".
Sir Michael told BBC Radio 4's Today programme that the UK government had had close discussions with the US over the past few days and had been given "advance notice of the President's final decision".
Sir Michael said the US strike had "targeted the airfield, the aircraft the support equipment that were involved, the Americans believe, in this gas attack and is designed to deter the regime from planning similar gas attacks".
He said the US "hasn't declared war" on Syria and the UK had not been asked to get involved: "The Americans have made it very clear the attack last night was limited, was narrowly focused, they did everything possible to minimise Syrian casualties, indeed to involve Russian personnel on that particular airfield."
He added: "It is Russia that has the influence over the regime that could bring this war to a halt if they chose to do so and I hope will learn from what happened last night and use its influence against Assad to bring this slaughter to a stop."
UK MPs rejected strikes against Syrian government forces in a 2013 vote and Sir Michael said there would have to be a vote in Parliament before the UK took part in any military action.
UK 'should urge restraint'
He stressed that the UK had not been asked to join the US action and was "involved in trying to get a political settlement in Syria and we will all be working harder to do that now".
But Labour Leader Jeremy Corbyn said: "Tuesday's horrific chemical attack was a war crime which requires urgent independent UN investigation and those responsible must be held to account.
"But unilateral military action without legal authorisation or independent verification risks intensifying a multi-sided conflict that has already killed hundreds of thousands of people."
He said the UK government "should urge restraint on the Trump administration and throw its weight behind peace negotiations and a comprehensive political settlement".
However the party's deputy leader Tom Watson told the Birmingham Mail the US strikes "appear to be a direct and proportionate response" and chemical attacks on civilians "must have consequences" while John Woodcock, who chairs Labour's backbench defence committee, described the US action as "proportionate" and said it "should have Labour's full support".
And former shadow foreign secretary Hilary Benn tweeted: "Let's hope Syria will now think twice before deciding to gas its own people again. Priority must be humanitarian assistance for civilians."
Liberal Democrat leader Tim Farron supported the US action and said the UK should be prepared to become involved militarily as well.
He said: "The British government, rather than just putting out a bland statement welcoming this, should now follow it up and call an emergency meeting of the Nato alliance to see what else can be done, be that more surgical strikes or no-fly zones.
"Evil happens when good people do nothing. We cannot sit by while a dictator gasses his own people. We cannot stand by, we must act."
But the SNP's Alex Salmond said the US strike "seems to dramatically reverse the previous stance of the Trump administration which was to partner Russia and tolerate Assad".
"If the position of the UK government is merely to back any US action whatever it may be then they will find themselves struggling to keep up with the twists and turns of the Trump administration," he said.
Former UKIP leader Nigel Farage, who appeared alongside Mr Trump on campaign rallies before his election, urged Britain not to get involved in any further air strikes.
He said: "I am very surprised by this.
"I think a lot of Trump voters will be waking up this morning and scratching their heads and saying 'where will it all end?'
"As a firm Trump supporter, I say, yes, the pictures were horrible, but I'm surprised. Whatever Assad's sins, he is secular."
US President Donald Trump called on "all civilised nations" to help end the conflict in Syria and branded Syrian President Bashar al-Assad a "dictator" who had "launched a horrible chemical weapons attack on innocent civilians".
The UK government has made renewed calls this week for diplomatic action in response to the chemical attack.
The US, UK and France had brought a resolution before the United Nations Security Council, demanding an investigation.
But on Wednesday, Downing Street had played down the prospect of military action, insisting "nobody is talking" about an armed response to the suspected chemical attack.