The Labour leader also called on Britain to push for an independent United Nations -led investigation to hold those responsible to account, saying: "Rather than further military action, what is urgently needed is a coordinated worldwide drive to achieve a ceasefire and a negotiated settlement under United Nations auspices".
"Britain should press for an independent UN-led investigation of last weekend's horrific chemical weapons attack so that those responsible can be held to account".
Speaking at Downing Street on Saturday morning, May said the strikes were "limited and targeted" and created to degrade the Syrian regime's ability to develop and use chemical weapons.
Corbyn also said countries involved should get around a negotiating table to find an end to the civil war by political means.
The Chair of Labour's backbench Foreign Affairs Committee said he was in support of the Prime Minister over his party's leader, saying: "It is welcome that the United Kingdom has taken this action and has joined its allies".
"They agreed to keep working closely together on the global response", the statement concluded.
"Bombs won't save lives or bring about peace", he said, adding that Britain should be leading the response and "not taking instructions from Washington and putting British military personnel in harm's way".
But rival politicians and some Conservative colleagues have called for a parliamentary vote before any British involvement. French President Emmanuel Macron said Thursday France has "proof" Assad had used chemical weapons and was working closely with the US on a possible response.
Diane Abbott, the shadow home secretary, went further, saying the Labour party believed there was no military answer to the Syrian crisis.
In a subsequent tweet on Thursday, the U.S. president said an attack on Syria "could be very soon or not so soon at all".
May released a statement confirming the strikes, which were carried out at 2am GMT on Saturday, just minutes after US President Donald Trump announced the air raid from the White House.
MPs are due to return to Westminster from the Easter recess on Monday - and a row is continuing between some MPs over whether a vote should take place in Parliament before any action is taken.
But he said it was "intellectually bankrupt" to expect the security services to lay out all the information they have.
He added: 'Theresa May should have sought parliamentary approval, not trailed after Donald Trump.