"The Americans should know that this was our first action," said parliament speaker Ali Larijani, after announcing overwhelming support for a package "to confront terrorist and adventurist actions by the United States in the region".
After the result was announced, lawmakers shouted: "Death to America."
A total of 240 parliamentarians out of 244 present voted for the bill.
It mandates the government to allocate an additional $260 million for the "development of the missile programme" and the same amount to the Revolutionary Guards' foreign operations wing, the Quds Force, state news agency IRNA said.
The Quds Force leads Iran's military role in Syria and Iraq.
Tehran says the measures violate a 2015 deal with world powers that eased sanctions in exchange for curbs on its nuclear programme.
Trump repeatedly threatened to tear up what he once called "the worst deal ever", but last month he backed away from a key campaign promise to withdraw from the nuclear agreement.
Iran's Deputy Foreign Minister Abbas Araghchi said the bill passed on Sunday had the support of the government.
The bill is "very smart particularly because it doesn't violate the nuclear deal and doesn't allow the other side to make excuses," he added.
"Iran boasts potential and actual options to confront hostile US actions".
The United States has had no diplomatic ties with the Iran since 1980, and Trump has halted the direct contacts initiated by his predecessor Barack Obama.
A string of close encounters between US ships and Iranian vessels in the Gulf in recent months has added to the tensions between the two countries.
Araghchi said that the Iranian bill was a far-reaching response to the measures passed by US Congress that Iranian media have called the "mother of sanctions" because they sum up all existing anti-Iran sanctions.
"Iran recognises the entire American military and intelligence forces as terrorist groups" for their "implicit and explicit support for terrorist groups" in the region, their role in creating the Islamic State group, and "the support for violators of fundamental humans rights especially the dictator and violent regimes," the bill's text said.
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