Boris Johnson says it would be very difficult for the UK to refuse the US if it asked for support in another military strike on Syria.
The foreign secretary also said MPs would not necessarily have a vote on any proposed joint action.
Pressed on his comments, the PM said it was a "hypothetical issue" as there were no plans for further strikes.
Labour leader Jeremy Corbyn said if the request was made to him as PM, he would ask the United Nations to intervene.
"I don't see how more bombing would help," he told the BBC.
The US carried out a missile strike against a Syrian air base earlier this month - days after a chemical attack that left 80 people dead and hundreds wounded.
Syria's President Bashar al-Assad denied his forces were responsible.
Mr Johnson claimed the Assad regime had "unleashed murder upon his own citizens with weapons that were banned almost 100 years ago".
And he told BBC Radio 4's Today programme: "I think it would be very difficult if the US has a proposal to have some sort of action in response to a chemical weapons attack.
"And if they come to us and ask for our support - whether it's with submarine-based cruise missiles in the Med... in my view - and I know it's also the view of the prime minister - it would be difficult for us to say 'no'."
Asked if the Commons would need to be consulted ahead of any military strike, Mr Johnson commented: "I think that needs to be tested."
Pressed on the comments later, Theresa May said it was a "hypothetical issue" as further strikes were not on the table.
She said Mr Johnson had been focussing on "working diplomatically to see if we can find a way now to persuade the backers of President Assad ... to work for a political transition away from President Assad for the future stability of ... Syria".
She added: "Boris is doing a great job as foreign secretary."
In recent years the convention has been that MPs get a vote on military action, but with Parliament about to dissolve ahead of a general election that could be put in doubt if the US launches fresh strikes in the next six weeks.
Mr Corbyn, who was highly critical of the latest US missile strike against Syria, said if there was a US request for the UK to back military action "all parties would have to be consulted".
He said: "We don't need unilateral action, we need to work through the UN, but above all we need to bend ourselves totally to getting a political settlement in Syria and allow the inspectors space to work, allow them to make sure we know who did that terrible chemical weapons attack and also recognise that the inspectors there are already destroying any stocks of chemical weapons that they find."
Analysis by BBC Diplomatic Editor James Landale
This is a departure because until now overt UK military action in Syria has been focused on attacking the so-called Islamic State group.
MPs voted to allow this, after a debate in December 2015.
Since then, the Ministry of Defence says, UK warplanes operating out of Cyprus have carried out 90 air strikes against IS targets.
There have been many other sorties over Syria in which UK aircraft and drones have gathered intelligence.
SNP foreign affairs spokesman Alex Salmond said Mr Johnson's comments were "significant" and "also dangerous", arguing that the government needs to seek parliamentary authority for military action.
"Boris Johnson's response to every single international situation is to agree or do whatever the Trump White House does - and I think the vast majority of the people in this country will look askance at having a 'mini-me' policy to President Trump," he told the BBC.
Liberal Democrat leader Tim Farron said: "The idea that the Conservatives are now increasingly beholden to Donald Trump is terrifying," adding that "a unilateral, illegal intervention would be utterly counterproductive."
But sources close to the foreign secretary told the BBC "there is no change in position", saying this is all a hypothetical situation and Mr Johnson was not ruling out a parliamentary vote if the US make a request for support.
In an interview on 7 April after US airstrikes on Syria, Defence Secretary Michael Fallon claimed the UK government was "not committed to military action in Syria".
While the law does not require the government to win a Commons vote before launching military strikes, Sir Michael said since 2003 the government had made it clear it would "go to Parliament to seek the authority" for action involving combat troops or aircraft.
In 2013, then Conservative prime minister David Cameron lost a Commons vote on possible UK military action against Syrian President Bashar al-Assad's government to deter the use of chemical weapons.
The government motion was defeated by 285 votes to 272, ruling out joining US-led strikes.