"The president has been clear that now is not the time for Congress to pass additional legislation on Iran," National Security Council spokeswoman Bernadette Meehan told ABC News. "If this bill is sent to the president, he will veto it."
Along with Sen. Tim Kaine, D-Va., Senate Foreign Relations Chairman Bob Corker, R-Tenn., introduced a bill this week that would allow Congress 60 days to review, and potentially reject, any deal to roll back U.S. nuclear sanctions on Iran.
In a statement issued by his office, Corker called the White House's veto threat "disappointing."
The framework for the current negotiations calls for an ultimate deal to "lift" nuclear sanctions on Iran, and some observers have concluded that would necessitate an eventual vote from Congress anyway, even if sanctions are only gradually eased in the nearer term.
Negotiations between Iran and world powers including the U.S., UK, France, Germany, Russia, and China have entered their final phase ahead of a March 31 deadline.
Secretary of State John Kerry told The Associated Press the sides had made "some progress" after his last meeting with Iranian Foreign Minister Javad Zarif this week.