US Defense Secretary Jim Mattis said Tuesday that President Donald Trump should consider sticking with the nuclear accord with Iran, which he said is in the US national interest.

Mattis's expression of support for the 2015 agreement curbing Iran's nuclear program was in sharp contrast with Trump's blunt assessment that the deal is an "embarrassment to the United States."

"If we can confirm that Iran is living by the agreement, if we can determine that this is in our best interest, then surely we should stay with it," told the Senate Armed Services Committee.

"I believe at this point in time, absent indication to the contrary, it is something that the president should consider staying with," he said.

Asked whether he believed the Iran deal was in the national interest, Mattis replied: "Yes, senator, I do."

Trump must notify Congress every 90 days whether he believes that Iran is abiding by the accord and whether lifting of sanctions against Tehran, as provided for under the agreement, remains in the US national interest.

He has so far certified that Iran is in compliance but has indicated that the next deadline on October 15 will be crucial.

Iran and the other signatories -- China, Russia, France, Britain and Germany -- defend the deal as a guarantee of the peaceful, non-military purposes of Tehran's nuclear program.

But in his speech last month to the UN General Assembly, Trump raised the prospect he might pull Washington out, calling the deal an embarrassment and warning, "I don't think you've heard the last of it."

He later told reporters he had reached a decision, but would not say what course of action he intends to take.

- Risks of not certifying -

Several senior US officials, as well as observers who oppose the deal, have said that if Trump does not certify Iran's compliance it would not necessarily mean either a US withdrawal, or the end of the pact.

In the event of non-certification, the law gives Congress 60 days to decide whether to reimpose on Iran sanctions lifted in 2015 as part of the deal. Washington could use that time to pressure its European allies to reopen negotiations with Tehran.

That would be risky, however.

Iran could interpret US non-certification -- or the imposition of new or renewed sanctions -- as a violation of the deal, and resume its banned uranium enrichment program.

Reimposition of sanctions by the US Congress would spell the demise of the agreement, according to European diplomats.

Neither Tehran nor the other signatories want to renegotiate the deal, although French President Emmanuel Macron has suggested trying to add "one or two pillars" to it as a compromise.

The Americans challenge several points of the agreement, beginning with the fact that the restrictions on Iran's nuclear program gradually fall away beginning in 2025.

They also are demanding that inspections of Iran's nuclear facilities by the International Atomic Energy Agency be extended to several military sites.

Beyond that, Washington argues that Iran is violating the spirit of the agreement by pressing ahead with a separate ballistic missile program and with its "destabilizing" activities in the Middle East, including Yemen and Syria.