Ministers said it was "highly likely" the Assad regime was responsible for a suspected chemical attack. "This legally questionable action risks escalating further", Corbyn, a veteran anti-war campaigner, said.
Assad and Russian Federation deny using chemical weapons, the trigger for the strikes early on Saturday.
Mr Corbyn has said parliament should be consulted before any military action.
No details of United Kingdom involvement in any military action in Syria were mentioned in the Downing Street statement.
But Carwyn Jones, Labour's First Minister of Wales, backed the action, as long as it was part of a wider plan to bring peace to the region. "It will just take more lives and spawn the war elsewhere".
The prime minister, who spoke to Trump about the need to deter chemical weapon use in Syria in a phone call Thursday, is facing pressure from all sides to seek the backing of parliament.
"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".
Britain will study the "options" with its allies if President Bashar al-Assad again uses chemical weapons against his people in Syria, but as yet there is nothing planned, Johnson also said on Sunday.
"They agreed to keep working closely together on the global response", the statement concluded.
North Atlantic Treaty Organisation allies have given the action their full support, secretary general Jens Stoltenberg said.
He added: "It's important that we understand the limits of what we are trying to do".
Shadow foreign secretary Emily Thornberry said taking military action against the Assad regime had been the "wrong thing to do".
David Cameron, May's predecessor, lost a parliamentary vote on air strikes against Assad's forces in 2013 when 30 Conservative politicians voted against action, with many Britons wary of entering another conflict after interventions in Iraq, Afghanistan and Libya failed to bring stability to the region.
"The reason they're not doing it is they are frightened they'll lose the vote".
He said it was "deeply alarming" to see the return of chemical weapons to the battlefield in Syria and the airstrikes was the "right thing to do" in "settling the determination to ensure these weapons cannot be used".
The White House insists that final decisions have still to be made.