Mr Trump’s administration has twice delayed a decision on whether to scrap the pinnacle of former President Barack Obama’s foreign policy, acknowledging that Iran is complying with the terms.
A new decision on Iran’s compliance must be sent to Congress by 15 October, when the tri-monthly certification period expires.
If the White House does not agree that Iran is in compliance, Congress will have 60 days to decide whether to slap Tehran with fresh sanctions - and the Republican-led house would be likely to vote to kill the deal.
Amid tensions over North Korea's nuclear and ballistic missile development, the deal's supporters worry its collapse could trigger a regional arms race, worsen Middle East tensions and discourage rogue states like North Korea from trusting Washington to keep its word.
Iranian President Hassan Rouhani, among other international leaders, has repeatedly said the deal cannot be renegotiated or annulled.
While Secretary Mattis has previously said he supports Mr Trump’s proposed review of whether Iran is “breaching the spirit” of the deal with non-nuclear warhead testing, he told a Senate hearing on Tuesday he believed it is the US’s security interests to maintain it.
“If we can confirm that Iran is living by the agreement, if we can determine that this is in our best interest, then clearly we should stay with it,” he said.
”I believe… absent indications to the contrary, it is something that the president should consider staying with,” he added.
The president’s campaign trail proposal to dismantle the nuclear deal - which lifted the international sanctions which have crippled Iran’s economy - was widely criticised for endangering an agreement which former Secretary of State John Kerry said “made the world a safer place.”
Since taking office in January he has repeatedly hinted he still intends to scrap it, although the administration has not yet laid out a broader Iran policy.
In his first address at the United Nations General Assembly last week, President Trump again called the deal between Iran and six world powers an “embarrassment”.
The White House has not commented on Secretary Mattis’ remarks.
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