The Trump administration will remain in the international nuclear deal with Iran for now, top national security aides said Sunday, a message of reassurance after allies, members of Congress and the Iranian regime criticized President Trump's decision to set conditions on further U.S. participation.

Trump's national security adviser, H.R. McMaster, said that the president's threat to cancel the Iran deal “set out a marker” for the United States and its allies to fix what he called “a weak deal that is being weakly monitored.”

“The president has made clear that he will not permit this deal to provide cover for what we know is a horrible regime to develop a nuclear weapon,” McMaster said during an appearance on “Fox News Sunday.”

“One of the real problems with this deal is we can’t really say with confidence that they’re complying,” McMaster said, accusing Iran of having “walked up to the line” and “crossed the line several times in terms of the restrictions.”

“This is not a trustworthy regime,” he said. “So much more comprehensive monitoring is in order.”

Asked what incentive Iran has to revisit the deal, McMaster said: “They have to revisit it because otherwise what you do is you just give the Iranians the opportunity to develop a nuclear capability. Their programs can advance and then they can go to industrial scale enrichment of uranium within a very short period of time and then bridge into a weapon, and that is just an unacceptable risk to the world.”

McMaster insisted that “the president’s not walking away from the deal yet” and wants to see “some real change.”

President Trump announced Oct. 13 that his administration would take new steps going forward to confront Iran. (The Washington Post)

Secretary of State Rex Tillerson said the president’s action on Iran is a “signal” to Congress and the other signers of the agreement, including Iran.

“If we don’t see improvement, there is no sense in staying in, and he has every intention of walking out,” Tillerson said on CBS's “Face The Nation.” The action Friday puts the onus on Congress to decide what to do next, including attempting to add provisions that would satisfy U.S. concerns, Tillerson said.

A separate new agreement among the international parties to the deal could “lay alongside” the existing 2015 pact, Tillerson said. He dismissed criticism that Trump’s opposition to the Iran deal as it stands would spoil chances for a similar international compact to address North Korea’s nuclear program.

“It would be pretty rich” for North Korea to doubt U.S. trustworthiness, Tillerson said with a smile. He said the diplomatic approach he is pursuing “will continue until the first bomb is dropped."

Sen. Lindsey O. Graham (R-S.C.) said Trump is taking the right approach to Iran and a deal the senator said he agrees is deeply flawed.

“The president ran on the idea that this was a bad deal for America, and he won,” Graham said.

He suggested he could support the approach favored by GOP Sens. Bob Corker (Tenn.) and Tom Cotton to add “triggers” for Iranian behavior that would lead to a return of U.S. sanctions suspended under the deal. That would require legislation, and some Democrats say it appears to be only a precursor to an eventual U.S. withdrawal from the deal.

Sen. Chris Murphy (D-Conn.), a member of the Foreign Relations Committee, said it is “an absolute fantasy” to believe that negotiations over the Iran deal will be reopened.

“The Iranians will not renegotiate it, and neither will the Europeans,” Murphy said on “Fox News Sunday." “And so if we were to pull out of this agreement, as the president is threatening, Iran would get everything they want. They would be able to restart their nuclear program, because we would be in violation of the deal. The Europeans would continue to grant them sanctions relief, their economy would continue to grow and they would look like the victim in the situation.”

Murphy also said that Iran is currently complying with the agreement.

“The White House is required to tell Congress if they are not, and they’ve submitted absolutely no submissions,” he said.

Hillary Clinton sharply criticized Trump on Sunday, saying his declaration “says America’s word is not good.”

Appearing on CNN’s “Fareed Zakaria GPS,” the former Democratic presidential candidate and secretary of state noted that others in Trump’s administration had advised against the move and that Trump was decertifying a deal “in the absence of evidence that Iran is not complying.”

“That is bad not just on the merits for this particular situation, but it sends a message across the globe that America’s word is not good,” Clinton said. “We have different presidents, and this particular president is, I think, upending the kind of trust and credibility of the United States’ position and negotiation that is imperative to maintain.”

“I know that Iran plays a game of aggressiveness and undermining of our interests and the interests in the region — there’s no argument about that,” Clinton said. “But my point has been and remains, I would much rather deal with Iran’s other bad behavior while not worrying at this moment about their nuclear program getting up and going again. And why on earth would we want two nuclear challenges in Iran and North Korea at the same time?”

That argument was also heard Sunday from Iranian Foreign Minister Mohammad Javad Zarif, who said the United States is becoming less credible as a partner.

“The whole reason we're looking at this Iran agreement is because of North Korea,” U.N. Ambassador Nikki Haley said during an appearance on NBC’s “Meet the Press.” “What we're saying now with Iran is don't let it become the next North Korea.”

Zarif, interviewed on the same CBS program, said Tillerson had not called him to preview Trump’s speech Friday, “and I didn’t expect him to.” Zarif, who led negotiations for Iran, said Trump is undermining global confidence in the United States. “The United States is no longer just unpredictable, but unreliable,” Zarif said in an interview in Tehran.