The bill, sponsored by the chairman of parliament's national security and foreign policy committee, was signed by 225 of the country's 290 MPs and faces a vote on Sunday.
"At the moment, the negotiating team is facing excessive demands from the United States," said chairman Alaeddin Boroujerdi.
"This bill is being introduced with the aim of supporting the negotiators... And to protect the red lines drawn up by the supreme leader."
First is the "complete and unified lifting on the day of agreement of all sanctions imposed through the UN Security Council, the US Congress and the European Union."
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That condition does not specify if it means the day a deal is struck, signed or implemented.
According to the EU and US, sanctions will only be lifted once international inspectors have verified that Iran's nuclear programme is peaceful, as per an outline agreement of April 2.
To ensure Iran's nuclear programme does not have military aims, the world powers are demanding an additional protocol allowing more stringent inspections of other facilities in Iran where nuclear activities may have been conducted.
Thirdly, the bill states: "No limit will be accepted on Iran acquiring peaceful nuclear knowledge and technology and the materials required for research and development."
Under the April 2 agreement, the EU and US both said Iran's research activities would have limits.