Of the members present, 240 parliamentarians out of 244 voted in favour of passing the bill.
As well, the bill allocates a budget of about $5 billion to what is termed as "reinforcing the country's defensive power, improving deterrent its power, countering terrorism, increasing Iran's diplomatic leverage and intelligence capabilities, safeguarding the regional stability, supporting the IRGC, development of nuclear propellers and boosting Iran's defensive capabilities against possible nuclear attacks".
Lawmakers gave the go ahead for the crafting of the bill which is aimed at countering "America's terrorist and adventurist actions", according to the state broadcaster IRIB.
Parliament Speaker Ali Larijani said the parliament's vote to approve the motion was just the first step, adding that if Washington proceeds with its anti-Tehran policies, the law will take effect.
The US legislation would impose mandatory penalties on people involved in Iran's ballistic missile program and anyone who does business with them.
Iran denies violating the United Nations resolution which endorsed the Tehran's 2015 nuclear deal, preventing them from conducting activities related to ballistic missiles created to deliver nuclear weapons.
Washington's new sanctions violate a 2015 nuclear deal with Iran both "in letter and spirit".
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.
Iran has launched ballistic missiles in tests, something it is allowed to do under the deal, despite American criticism.
The Iranian legislation must pass a second vote before submission for final approval.
But last month he backed away from his pledge to withdraw from the agreement.
A number of recent close encounters between U.S. ships and Iranian vessels in the Gulf have added to the tensions between the two countries.