WASHINGTON — In the midst of a nuclear crisis with North Korea, the Trump administration signaled on Tuesday that it is paving the way for a simultaneous standoff with Iran, suggesting it could refuse to certify that Tehran is complying with the 2015 nuclear accord. But the administration could leave it up to Congress to decide whether to withdraw from the deal.

In a speech at the conservative American Enterprise Institute, Ambassador Nikki R. Haley, the United States representative to the United Nations, presented the administration’s argument that Iran was in violation of the spirit, if not the letter, of the agreement. But by not actually withdrawing from the accord, President Trump could avoid a direct breach with the other signatories — Britain, France, Germany, Russia and China — which appear to agree with international inspectors that Iran has complied with its direct obligations in the agreement.

Administration officials said there was little doubt now that Mr. Trump would not certify Iran’s compliance again, as he is required to do every six months. The president said as much in July, when he reluctantly signed the most recent certification. “If it was up to me, I would have had them noncompliant 180 days ago,” Mr. Trump said.

On Tuesday Ms. Haley went even further, saying that Mr. Trump would be entirely justified if he decided to decertify an accord he had declared during the campaign was “the worst deal ever negotiated.”