President Donald Trump is due on May 12 to announce his decision about whether America will stay in the historic pact, as US and European diplomats work on a supplemental deal to address his concerns.

"I can assure you there has been no decision made on any withdrawal from JCPOA," Mattis said of the deal, which is officially known as the Joint Comprehensive Plan of Action.

"The discussions are ongoing in the national security staff and those of us who are charged with that responsibility of giving the president advice. It's going on today as we speak," Mattis told the Senate Armed Services Committee.

Though he thinks the deal is flawed, Mattis has previously said he supports America staying in it, telling lawmakers in October it is in the US national interest to do so.

But Mattis offered no such support Thursday.

"There are obviously aspects of the JCPOA... that can be improved on. We are working with our European allies on it at this time, and again at this time the decision has not been made whether we can repair it enough to stay, or if the president if going to decide to withdraw from it," he said.

Trump, who campaigned on scrapping the Iran deal, has branded it as "insane" and the "worst" in history.

"This is a deal with decayed foundations. It's a bad deal, it's a bad structure. It's falling down," Trump said Tuesday.

"We're going to see what happens on the 12th."