Trump, who walked out of a nuclear accord with Iran and instead slapped sweeping sanctions, last month authorized a strike on the Islamic republic after it shot down a USA spy drone - but called it off at the last minute.
However, a similar amendment to the NDAA failed in the Senate last month, as it received only 50 votes - ten fewer than the 60 votes needed to pass.
Pelosi has cast the sniping among House Democrats as a threat to achieving common goals, one of them to defeat Trump's bid for reelection.
This latest (and most public) bout of Democratic infighting was set off in part by Speaker Nancy Pelosi's comments to New York Times columnist Maureen Dowd about "the Squad"--freshmen congresswomen Alexandria Ocasio-Cortez, Ilhan Omar, Rashida Tlaib and Ayanna Pressley. The measure passed, but liberal House Democrats said the bill didn't do enough to protect migrant children held in federal detention centers amid reports of poor conditions. Her remarks came after Ocasio-Cortez's chief of staff criticized Pelosi and compared moderate Democrats to segregationist senators.
Ocasio-Cortez, Tlaib and Reps.
(L-R) Representatives-elect Alexandria Ocasio-Cortez (D-N.Y.), Debbie Mucarsel-Powell (D-Fla.) Abby Finkenauer (D-Iowa), and Sharice Davids (D-Kan.) join with other newly elected members of the House of Representatives for an official class photo of new House members at the U.S. Capitol in Washington on November 14, 2018. "I knew we'd see a system that was overwhelmed". It also allows US detainees at a military base in Guantanamo Bay to be moved to the United States, something Republicans have said represents a back-door effort to force the Administration to close the controversial detention facility.
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"Our national security is not a game".
Senator Tom Udall, one of the sponsors of the Senate measure on Iran, said the Senate had sent a "clear message" to Trump, even though the measure was blocked.
Trump last month came close to launching strikes on Iranian targets following Tehran's downing of an American reconnaissance drone that Iran says breached its airspace.
"Our bill isn't just good, it's better than the ones that the Republican Party has put together, because we believe the Pentagon should be accountable", Smith continued.
The Trump administration has promised to veto the House measure.
Rep. Chip Roy, R-Texas, mocked Democrats' border trip, accusing them of posing "next to an empty parking lot while making up hyperbole for clips, Twitter followers and cynical politics". Among them was a 251-170 tally to require Trump get authorisation from Congress to conduct military strikes against Iran, along with a repeal of a 2002 law authorising the war in Iraq.
They also voted in favor of suspending for one year the sale of air-to-ground munitions to Saudi Arabia and the United Arab Emirates, one of several efforts in the bill to deny weapons and limit USA support for Saudi-led military operations in Yemen's civil war.