The nuclear deal (also referred to as JCPOA), signed in 2015 by Iran and the six powers including the United States, led to the lifting of most sanctions against Tehran in return for curbs on its nuclear programme.
However, the U.S. Treasury's Office of Foreign Assets Control imposed sanctions on six Iranian firms in late July for their role in development of ballistic missile program after Tehran's launch of a rocket capable of putting a satellite into orbit.
The U.S. Senate also voted on the same day almost unanimously to impose new sanctions on Iran, Russia and North Korea. The sanctions in that bill also target Iran's missile programs as well as human rights abuses.
"Iran's JCPOA supervisory body assessed the new U.S. sanctions and decided that they contradict parts of the nuclear deal," Iran's speaker of parliament Ali Larijani was quoted by the Tasnim news agency as saying.
"Iran has complained to the U.N. Security Council for the breach of the JCPOA by America," he added.
Iranian media said on Monday that the government has decided on measures in reaction to the U.S. sanctions and that President Hassan Rouhani will be announcing them soon to related ministries.
U.S. President Donald Trump issued a veiled threat against Iran last week, warning Tehran to adhere to the terms of the nuclear accord or face "big, big problems."
The Trump administration certified Iran as being in compliance with the nuclear deal, even though Trump has called the agreement negotiated by his Democratic predecessor "the worst deal ever."