President Trump is now fully engaged in two nuclear confrontations, one with Iran over a nuclear accord he finds an “embarrassment” and the other with North Korea that is forcing the Pentagon to contemplate for the first time in decades what a resumption of the Korean War might look like.

The dynamics of those cases are entirely different, but they are also oddly interdependent. If Mr. Trump makes good on his threat to pull out of the 2015 nuclear agreement with Iran, how will he then convince the North Korean leader, Kim Jong-un, that America will honor the commitment to integrate North Korea into the world community if only it disarms — the demand Mr. Trump made from the podium of the United Nations.

The fiercest defenders of the Iran deal argue that Mr. Trump’s team has not thought about how his threats to Tehran resonate 4,000 miles away in Pyongyang, especially since Iran has held up its end of the agreement.

“If the president pulls back on the Iran deal, given Iranian compliance” with its terms, said Wendy R. Sherman, the chief negotiator of the accord, “it will make diplomacy on North Korea almost impossible because U.S. credibility will be shot.”