"We're going to stay in," Tillerson said in an interview with CNN's Jake Tapper on "State of the Union," though he left open the possibility that the US could seek another agreement.
"We're going to work with our European partners and allies to see if we can't address these concerns," he added.
Trump on Friday said Iran
was violating the agreement and threatened to pull out of the deal, pushing the issue to Congress. Tillerson has said in the past Iran was in "technical compliance" with the deal.
Asked to square these two claims, Tillerson said Iran had committed technical violations of the deal, but that the agreement was structured in a way to give Iran significant time to remedy its violations.
"They have remedied the violations, which then brings them back into technical compliance," Tillerson said.
Tillerson said Trump had demanded a broader strategy on Iran and said the US was focused on more issues than simply Iran's potential nuclear ambitions, citing the nation's ballistic missile program and support for groups adversarial to the US throughout the Middle East.
"What the President wants is a more comprehensive strategy," Tillerson said.
He said the US was working to address issues it had with the multilateral agreement and anticipated that might require a new deal.
"Let's see if we cannot address the flaws in the agreement by staying within the agreement, working with the other signatories, working with our European friends and allies within the agreement," Tillerson said. "But that, as I said, may come in a secondary agreement as well."
Tillerson cataloged the US' inability to prevent North Korea from obtaining nuclear weapons, and said the Trump administration's efforts on Iran were to prevent a situation similar to the one on the Korean peninsula from unfolding in the Middle East.
"We don't want to find ourselves in that same position with Iran," Tillerson said.
Administration echoes demands
In an interview on NBC, US ambassador to the United Nations Nikki Haley said Trump's decisions on the nuclear agreement were directly related to North Korea. She said Trump was telling the North Koreans, through these moves, that the US would not make a bad deal to curb the North Korean nuclear program.
"What we're saying now with Iran is don't let it become the next North Korea," Haley said.
She offered similar commentary on the Iran deal, saying she believed the US would stay in it for the time being despite her staunch criticism of it and what she viewed as its limitations.
Lt. Gen. H.R. McMaster, Trump's national security adviser, said on "Fox News Sunday" that the administration is upholding its end of the deal and would stay in it while demanding gains through Congress and potentially by forging an additional agreement with Iran.
"Let's work on, as Secretary Tillerson has said, a deal that can lay alongside the (Iran deal) and address its fundamental flaws," McMaster said.