Johnson said it would be "very difficult to say no" if the US sought British help for a military mission against the forces of Syrian President Bashar Assad.
British lawmakers in 2013 rejected a request by then- Prime Minister David Cameron to authorize UK airstrikes in response to Assad's use of chemical weapons. Britain is part of an international coalition targeting the Islamic State group in Syria, but has not taken military action against Assad.
Parliament will be dissolved next week ahead of Britain's June 8 election, so lawmakers would not be able to vote on a request for military assistance before then.
President Donald Trump ordered a cruise missile attack against a Syrian air base earlier this month in response to Assad's apparent use of a banned nerve agent against a rebel- controlled area.
Johnson's remarks appeared intended to signal to voters that the Conservative government is tough on security and defense. He contrasted the stance to that of opposition Labour Party leader Jeremy Corbyn, a foreign-policy dove who wants Britain to give up its nuclear weapons.
Writing in The Sun newspaper, Johnson called Corbyn "a mutton-headed old mugwump" with "no grasp of the need for this country to be strong in the world."
Corbyn said he would not be "reduced to personal name- calling," and said the priority for Syria was finding a political solution to the conflict.
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