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 bill allows for a boost in spending on Tehran's missile program and the Islamic Revolution Guards Corps' defense mechanism. It also comes as a North Korean-announced deadline to fire missiles into the waters around Guam approaches.
"The Americans should know that this was our first action to confront terrorist and adventurist actions by the United States in the region", parliamentary speaker Ali Larijani said after the vote.
Iranian officials deem the anti-Iran sanctions over its ballistic missile program and alleged "support for terrorism" in violation of the spirit, if not the letter, of the JCPOA.
In response to the launch, President Trump signed a bill outlining new sanctions against several Iranian groups, freezing funds and outlawing USA citizens from doing businesses with the targets.
Deputy Foreign Minister Abbas Araqchi, who is the head of an Iranian commission tasked with monitoring the agreement's implementation, told MPs that the government backed the bill which he described "very strong".
He added that the bill will be supported by the government of President Hassan Rouhani, as it is required to pass a second reading before being submitted to the Guardian Council for final approval.
Tensions between Tehran and Washington have grown since President Trump took office.
Tehran says the measures violate a 2015 deal with world powers that eased sanctions in exchange for curbs on its nuclear programme. A string of close encounters between U.S. ships and Iranian vessels in the Gulf in recent months has added to the tensions between the two countries. Tehran says its missile program does not breach a United Nations resolution which endorsed the nuclear deal.