In the statement read out in the Sunday session of the parliament, more than 200 lawmakers emphasized that such behavior by the US, which cannot be called anything but "deception", will only lead to mistrust between the two negotiating sides.
The Iranian MPs further called on the country's negotiating team involved in the nuclear talks with the Group 5+1 (Russia, China, the US, Britain, France and Germany) to brief them on the final results of the negotiations.
The US Senate passed the bipartisan bill on Thursday by a 98-1 vote. It is expected to pass in the House, and has US President Barack Obama's support.
The White House originally opposed the bill, proposed by Senate Foreign Relations Committee chairman Bob Corker (R-TN), until some of its provisions were revised in a compromise deal with the committee's ranking democrat, Ben Cardin (D-MD) last month.
Iran and the Group 5+1, also known as E3+3 or P5+1, are in talks to hammer out a lasting accord that would end more than a decade of impasse over Tehran's peaceful nuclear program.
On April 2, the two sides reached a framework nuclear agreement in Lausanne, Switzerland, with both sides committed to push for a final deal until the end of June.
Diplomats from Iran and the EU wrapped up the latest round of negotiations in New York on Tuesday and are slated to resume the talks in Vienna on May 12 to press on with the task of drafting the comprehensive deal.