The motion was passed during an open parliamentary session on Sunday morning.
The US legislation would impose mandatory penalties on people involved in Iran's ballistic missile program and anyone who does business with them.
The measure was voted for by 240 out of 244 MPs present.
Parliamentarians approved the outlines of the bill to "counter America's terrorist and adventurist actions in the region" as some chanted "Death to America" after the vote results were announced.
The move follows a spike in tensions between Tehran and Washington since US President Donald Trump took office in January with a vow to get tough on the Islamic republic.
The bill mandates the government to allocate an additional US$260 million for the "development of the missile programme" and the same amount to the Revolutionary Guards's foreign operations wing, the Quds Force, state news agency IRNA said.
It will also require Iran's government and armed forces to draw up a plan to counter USA violations of human rights around the world and to support Iranian bodies and individuals affected by sanctions.
He praised the bill, saying it "was designed wisely so that it does not violate the (nuclear deal) and provide excuses for opposing sides".
Abbas Araghchi, a deputy foreign minister and senior nuclear negotiator on hand for the vote, said a moderate President Hassan Rouhani's government would support the bill.
The deal eased sanctions on Iran in exchange for curbs to its nuclear programme and was endorsed by a United Nations resolution.
He went on to say that according to the law, the Iranian administration is obliged to monitor the U.S. government's anti-Iran measures and counteract them accordingly.
Washington and European countries that negotiated the Iran nuclear deal have called the missile tests violations of the spirit of the 2015 accord, but not its letter.
The bill must now pass a second vote before being submitted to a clerical body for final approval and passage into law.