"The recent Senate bill is indicative of a new case of extremism which we have experienced time and again under the cover of democratic gestures," the MPs said in a statement.
"Under the rules of international negotiations, such an attitude has no name but deceit and will have no outcome but mistrust,” the signatories added.
They called on Iranian nuclear negotiators to react "appropriately" to the Senate bill and take it "seriously" into consideration throughout nuclear talks between Iran and six global powers.
The statement called for an accurate assessment of the behavior of the P5+1 group of countries, particularly the U.S., with regard to the ongoing nuclear talks.
It emphasized that inspections by the International Atomic Energy Agency (IAEA) must be conducted in accordance with international regulations.
The legislators also took the U.S. to task for using the language of threat, saying the Iranian negotiating team should give Washington a response it deserves.
The U.S. Senate on Thursday overwhelmingly passed a piece of legislation which will make it possible for Congress to review and potentially reject a final deal with Iran over its nuclear program.
The bill gives Congress 30 days to review a final nuclear deal after Iran and the P5+1 countries reach such an agreement, and during that time bars President Barack Obama from temporarily waiving any US sanctions on Iran that were passed by Congress.
Iran and the P5+1 group of countries -- the United States, Britain, France, Russia, China and Germany -- reached a mutual understanding on the parameters of a comprehensive agreement over the Islamic Republic’s nuclear program in Lausanne, Switzerland, on April 2.
Iran and the six-party group have agreed to finalize a comprehensive deal on Tehran’s nuclear program by the end of June.