President Trump warned that Iran is not "living up" to the "spirit" of its international nuclear deal at a press conference on Thursday.

"They are doing a tremendous disservice to an agreement that was signed. It was a terrible agreement, it shouldn't have been signed, it shouldn't have been negotiated the way it was negotiated," Trump said as he stood next to Italian Prime Minister Paolo Gentiloni in the White House's East Room.

"They are not living up to the spirit of the agreement, I can tell you that. And we are analyzing it very carefully, and we will have something to say about it in the not-too-distant future."

Trump bashed the Iran deal as too weak throughout the campaign, carrying that stance into office.

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Secretary of State Rex Tillerson told Congress in a letter Tuesday that Iran is still meeting its commitments under the deal. But the administration has also been stepping up its rhetoric on Iran and vowing to thoroughly review the agreement.

On Wednesday, Tillerson blasted Iran for "alarming and ongoing provocations that export terror and violence, destabilizing more than one country at a time."

He went on to argue that "an unchecked Iran has the potential to travel the same path as North Korea, and take the world along with it."

"The Trump administration is currently conducting a comprehensive review of our Iran policy," he added.

"Once we have finalized our conclusions, we will meet the challenges Iran poses with clarity and conviction."