On a largely party-line vote, the House backed the measure 249-176. It calls for prohibiting the Obama administration from buying more of Iran's heavy water, a key component in certain nuclear reactors.
The White House has said removing the country's surplus heavy water denies Tehran access to a material that may be stored for potential nuclear weapons production.
The U.S., other world powers and Iran finalised the nuclear pact on July 14, 2015, after nearly two years of intense negotiations.
President Barack Obama would veto the House bill if it reaches his desk, according to the White House. But Republicans said Iran should be punished for continuing to manufacture heavy water, not rewarded with millions of U.S. taxpayer dollars that may end up being used to support terrorism or Tehran's ballistic missile program.
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"Why are we giving the seal of approval to Iran's heavy water production?" asked Rep. Ed Royce, R-Calif., the chairman of the House Foreign Affairs Committee.
The bills have antagonised Democrats, who have accused the GOP of jettisoning bipartisanship in favor of election-year politics.
They said both parties have worked in the past to address Iran in a way that demonstrated unity instead of dissension.
Rep. Eliot Engel, D-N.Y., who opposed the nuclear deal, said he agreed the U.S. Shouldn't be buying Iran's heavy water. But Republican leaders wanted "political theatre," he said, and they hustled Kansas Rep. Mike Pompeo's bill to the House floor and barred any amendments to the legislation.