Iran is not "living up to the spirit" to the nuclear agreement, President Donald Trump said Thursday, as he continued to slam the accord as "a terrible agreement."

"They are doing a tremendous disservice to an agreement that was signed," Trump said at a news conference with Italian Prime Minister Paolo Gentiloni at the White House. "It was a terrible agreement.

"It shouldn't have been signed. It shouldn't have been negotiated the way it was negotiated."

Secretary of State Rex Tillerson on Wednesday accused Tehran of "alarming ongoing provocations" to destabilize countries in the Middle East and of undermining U.S. interests in Syria, Iraq, and Lebanon.

"An unchecked Iran has the potential to travel the same path as North Korea and to take the world along with it," Tillerson said.

He declared the 2015 Iran nuclear deal failed to achieve its stated objective of preventing Tehran from becoming a nuclear state.

Tillerson spoke after the State Department certified to Congress that Iran was currently in compliance with its obligations under the agreement.

Trump, who repeatedly blasted the Iran accord during the president campaign, kept up the attacks Thursday.

"I'm all for agreements, but that was a bad one, as bad as I've ever seen negotiated," he said. "They are not living up to the spirit of the agreement.

"We're analyzing it very, very carefully, but Iran has not lived up to the spirit of the agreement — and they have to do that."