The move would not withdraw the US from the deal but give Congress 60 days to decide whether to do so by re-imposing sanctions.
Under the 2015 accord, Iran agreed to freeze its nuclear programme in return for the partial lifting of sanctions.
President Trump has been a longstanding critic of the deal and pledged to scrap it during his campaign.
Congress requires the US president to certify every 90 days that Iran is upholding its part of the agreement. Mr Trump has already recertified it twice.
Speculation that Mr Trump might refuse to recertify the deal has caused alarm among US allies and some members of his own administration.
Defence Secretary James Mattis told a Senate hearing earlier this month it was not in the national interest to abandon it.