The bill would allocate about $260 million each to Iran's ballistic-missile program and the Quds Force, the external branch of the IRGC that is said to be active in Syria and Iraq.
The vote came after fresh U.S. sanctions in July against Iran, targeting Tehran's missile programme.
The legislation is a reaction to a bill ratified recently in the US Senate allowing Washington to impose non-nuclear sanctions against Iran's missile program and its Revolutionary Guard (IRGC) force. During Sunday's voting session, 240 out of 244 legislators approved the missile spending bill.
The plan would require Iran's government and armed forces to draw up a strategy to counter United States violations of human rights around the world, and to support Iranian bodies and individuals affected by USA sanctions.
"The bill has very wisely tried not to violate the JCPOA [Joint Comprehensive Plan of Action] and also give no chance to the other party to manipulate it", Deputy Foreign Minister Abbas Araqchi said, as cited by IRNA news agency.
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Iranian officials have repeatedly said Iran's missile program is for deterrent purposes.
A second vote will now take place on the bill before it is submitted to a clerical body for final approval.
The legislators stressed that the bill does not violate the 2015 nuclear deal between Iran and major world powers, but accused Washington of attempts to "kill" the landmark agreement.
Iran denies developing ballistic missiles created to carry nuclear weapons in violation of the agreement and has accused the U.S. of breaking its word by imposing fresh sanctions. A string of close encounters between United States ships and Iranian vessels in the Gulf in recent months has added to the tensions between the two countries.