WaPo notes that this could likely lead to tougher sanctions against Iran, as the Trump administration blames the country for terrorist activity in the Middle East.
Lawmakers would have 60 days to decide whether to reimpose sanctions that were suspended under the agreement.
Opposition to the deal was a major part of his campaign past year.
The president addressed the reporters and said, "You guys know what this represents?"
Donald Trump has cryptically warned that we are living in the "calm before the storm" - but has refused to explain what that means.
A reporter asked, "What's the storm, Mr. President?" Trump grinned mischievously and waved his hand in a semi-circle as the military leaders flanked him.
Democrats argued that Trump should certify the agreement, warning that the administration's ability to press Iran on other activities it objects to would be compromised - rather than enhanced - if the U.S. threw the future of the agreement into question.
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Asked on October 5 about his planned decision, Trump said, "You'll be hearing about Iran very shortly".
"In North Korea, our goal is denuclearisation", he said.
And on Tuesday Defense Secretary James Mattis said he believes it's "in our national security interest" to remain in the deal.
He responded: "You'll find out".
Tensions are also high between the USA and North Korea.
In a speech last month at the United Nations, Trump warned that the United States would "totally destroy" North Korea if needed to defend itself or US allies.
Previously, Mr. trump described the agreement signed by Iran, the US, Britain, France, China, Russia and Germany as "one of the worst deals I have ever seen".
"I think that the president is the one that's keeping the world from chaos", she claimed.