The vote on Thursday was 219 to 212, largely along party lines, in the House, where Trump's fellow Republicans control a narrow majority of seats. Two Republicans voted in favour of the resolution and four Democrats voted against it.
Opponents accused Democrats of taking the issue to a vote only because they oppose Trump, putting Americans at increased risk.
"We all know that we wouldn't be here today if the president's name wasn't Donald Trump," Representative Rick Crawford of Arizona, the Republican chairman of the House Intelligence Committee, said during debate on Wednesday.
Sponsors of the resolution described it as a bid to take back Congress' responsibility to authorise war, as spelled out in the US Constitution.
The US and Israel launched attacks on Iran on Saturday, a conflict that has killed more than 1000 people, including at least six US service members, and caused damage and instability throughout the Middle East.
Supporters said the resolution, by requiring Trump to come to Congress for a war authorisation, would force him to explain to Americans why the US is fighting and how it might end.
"This is a war of choice, launched by this administration without authorisation, without clearly stated objectives or a defined endgame, and without explaining how they intend to keep Americans safe," said Representative Gregory Meeks of New York, the top Democrat on the Foreign Affairs Committee.
Just before the resolution vote, House members from both parties overwhelmingly passed a measure "Reaffirming Iran remains the largest state sponsor of terrorism."
The vote would not have stopped the conflict even if the House had voted yes.
To go into effect, the resolution would also have had to pass the Senate and garner the two-thirds majorities needed to override Trump's expected veto.
The Senate, also narrowly controlled by Trump's party, backed his military campaign against Iran in a vote on Wednesday, voting to block a bipartisan resolution similar to the measure passed by the House.
The votes this week are not the end of the matter. The War Powers Resolution of 1973, which provides for votes on the resolutions, says a president can only involve the military in an armed conflict when Congress has declared war or provided specific authority or in response to an attack.
Trump and his Republicans have argued that Iran posed an "imminent threat" so that his actions were legal under that law.
However, the War Powers measure also requires unauthorised military actions to be terminated within 60 days, giving the Trump administration a deadline at the end of April to seek Congress' approval.
