The resolution was initiated by Republicans as a veiled criticism of President Barack Obama, who has been reluctant to criticize Tehran's handling of disputed elections that left hard-liner President Mahmoud Ahmadinejad in power.
Rep. Mike Pence, who co-sponsored the resolution, said he disagrees with the administration that it must not meddle in Iran's affairs.
"When Ronald Reagan went before the Brandenburg Gate, he did not say Mr. (Mikhail) Gorbachev, that wall is none of our business," said Pence, R-Ind., of President Reagan's famous exhortation to the Soviet leader to "tear down that wall."
Democrats, who are quick to voice their support for Israel anytime the Jewish state is seen as under siege, easily agreed to push through the mildly worded resolution.
Rep. Howard Berman, chairman of the House Foreign Affairs Committee and co-sponsor of the resolution, said "it is not for us to decide who should run Iran, much less determine the real winner of the June 12 election.
"But we must reaffirm our strong belief that the Iranian people have a fundamental right to express their views about the future of their country freely and without intimidation," added Berman, D-Calif.
Sens. John McCain, R-Ariz., and Joseph Lieberman, I-Conn., have proposed a similar measure in the Senate, although a vote was not certain.
The policy statement expresses support for "all Iranian citizens who embrace the values of freedom, human rights, civil liberties and rule of law" and affirms "the importance of democratic and fair elections."
It also condemns "the ongoing violence" by the government and pro-government militias against demonstrators, as well as government "suppression of independent electronic communications through interference with the Internet and cell phones."
Congress—particularly the 435-member House—frequently weighs in on foreign policy matters, when a similar message from the State Department or the White House would be considered confrontational. Such resolutions have no practical effect other than to express the opinion of lawmakers and try to influence the administration in power at the time.
The legislative branch's say so in foreign affairs has receded over time, the residue of growing executive branch power.
Rep. Ron Paul, a Texas libertarian who often speaks out against what he regards as government meddling, cast the sole opposing vote.
Obama, whose goal is to engage Tehran in the hopes of blunting its perceived ambition of a nuclear weapon, has stayed mostly neutral on the election dispute, talking in parsed, measured terms, about the aspirations of the Iranian people to have their voices heard.
Obama told CNBC this week that "when you've got 100,000 people who are out on the streets peacefully protesting and they're having to be scattered through violence and gun shots, what that tells me is the Iranian people are not convinced of the legitimacy of the election."
Obama also said that it was "not productive, given the history of U.S.-Iranian relations, to be seen as meddling."
Iranians have long blamed the CIA for helping topple the elected government of Mohammad Mosaddeq in 1953 and replacing him with the late Shah Mohammad Reza Pahlavi.