The Iranian and North Korean nuclear programs, drastically different but often spoken of in the same breath, are now being thrust together, as President Trump’s determination to kill the landmark 2015 accord limiting Tehran’s capabilities is colliding with his scramble to reach a far more complex deal with Pyongyang.

For years, as the Iranians watched the North Koreans build an arsenal and make deals with the West only to break them, they learned what the world was prepared to do — or was unwilling to risk — to stop them. More recently, the North Koreans picked apart what Tehran got in return for agreeing to a 15-year hiatus in its nuclear ambitions, weighing whether the promised economic benefits were worth giving up its nuclear capabilities.

The North will be watching especially closely in May, when Mr. Trump will face another deadline on deciding whether to abandon the Iran deal, which he has called a “disaster.”

The same month, if all goes as Mr. Trump plans, he will head into a face-to-face negotiation with North Korea’s dictator, Kim Jong-un — the first time an American president has ever spoken with the leader of that country — confident in his ability to do what his predecessors could not: persuade the North Koreans to denuclearize.

“The ironies abound,” said Robert S. Litwak, the director of international security studies at the Woodrow Wilson Center for International Scholars and the author of “Preventing North Korea’s Nuclear Breakout.”

“The man who wrote ‘The Art of the Deal’ has staked out a position that the Iran deal was the worst one in history,” he added. “And now he has to show that he can do much better, with a far harder case.”

On Sunday, the C.I.A. director, Mike Pompeo, speaking on the CBS program “Face the Nation,” set an extraordinarily high bar for his boss, if he ever gets to that negotiation.

Mr. Pompeo acknowledged that Mr. Trump, given his disparagement of the Iran deal reached by the Obama administration, will have to get a better deal out of Mr. Kim. “I think that’s the case,” he told the host, Margaret Brennan, adding that he thought Mr. Trump would be negotiating from a greater position of strength.

That is a debatable notion. Mr. Kim has driven the pace of this diplomatic effort so far, and American officials have conceded surprise at his boldness. And if Mr. Trump pulls out of the Iran deal, Mr. Kim may well wonder why he should negotiate with the United States if a subsequent president can simply pull the plug on any agreement.

By statute, Mr. Trump must decide by May 12 whether to make good on his threat to exit the Iran deal. American officials have said Mr. Trump could pull back if European allies agree to unilaterally crack down on Iran’s missile development — which is not covered by the nuclear deal — and begin a process to make the limits on Iran’s ability to produce nuclear material permanent.

The British and the French are reluctantly going along, though they say they fear that unilateral demands would blow up an arrangement that is working. German officials are balking, saying that extending the duration of the deal would require new negotiations, and new concessions.

Yet if Mr. Trump sticks with the agreement — as his top aides have quietly urged him to do — he faces a different challenge. While he will have to negotiate a deal with the North Koreans that is even stricter than the Iranian one that he has denounced as naïve, insufficient and dangerous, that task will be made all the harder by the fact that Pyongyang, unlike Tehran, actually possesses nuclear weapons.

North Korea has at least 20 by some estimates, or upward of 60 by the count of the Defense Intelligence Agency. Iran has never produced one.

North Korea produces both plutonium and uranium, and the C.I.A. suspects that some of it is produced at hidden sites. Iran gave up about 97 percent of its stockpile of low-enriched uranium, the material that the world feared it would use to “break out” of any agreement and build a bomb.

Even with the most rigorous inspection regime, it will be hard to assure that the North Korean program is really dead. Faced with similar suspicions, Iran agreed to let inspectors roam the country. North Korea never has: Before international inspectors were thrown out of the country, they were limited to living and working at one site, the main nuclear reactor at Yongbyon.

And while the Iran deal required months of secret talks followed by two years of public negotiations, but was aided by a unified stance among the United States, the Europeans, China and Russia. So far, none of those conditions exist in dealing with North Korea.

“If the president gets the North Koreans just to stop what they are doing, and perhaps get a timetable for future action, that would be a huge step in slowing the North Koreans’ program,” said Christopher Hill, who negotiated the last major deal that the United States had with North Korea, under the George W. Bush administration. “But it still wouldn’t be close to what Iran agreed to do.”

Part of the problem is that North Korea’s experience with its nuclear program is long and deep, which has left it adept at reversing even concessions that seemed large at the time.

When a 1994 agreement during the Clinton administration barred it from one pathway to the bomb, it struck a secret deal with the head of Pakistan’s nuclear program, Abdul Qadeer Khan, and learned another.

When Mr. Hill, now at the University of Denver, negotiated an accord at the end of the Bush administration, the North blew up its cooling tower at the Yongbyon reactor as evidence of its seriousness. It made for great television. But it did little to slow the nuclear program — the reactor has been back up and running for years.

Mr. Trump’s problem goes deeper. His two major complaints about the Iran deal are that it is not permanent and that it is not broad enough — it does not deal with Iran’s weapons shipments to Hezbollah, its support of Syria’s president, Bashar al-Assad, or its human rights abuses. Matching those requirements in a North Korea deal would make it all the harder to reach.

“In the North Korea case,” Mr. Litwak said, “no one has yet said what the scope of a deal would be, but if you look at the Iran deal critique, presumably it would have to solve a lot more than just our nuclear problems.”

That could include stopping the North’s export of chemical weapons to Syria, and its nuclear and missile exports. It might also include eliminating the thousands of conventional artillery weapons along the demilitarized zone that are aimed at Seoul.

And then there is the problem of North Korea’s gulags: At the State of the Union address this year, Mr. Trump invited a North Korean who had escaped to the South, suffering horrific injuries along the way.

Secretary of State Rex W. Tillerson, who was caught by surprise when Mr. Trump agreed to sit down with Mr. Kim, has warned that any negotiation will be long and drawn out. This first meeting between Mr. Trump and Mr. Kim, if it happens, would simply be to build trust and set broad directions.

So far, Mr. Trump is talking only about what the North Koreans would give up in any negotiation. The North Koreans are bound to demand that the United States withdraw American troops from South Korea, and perhaps that it agree to a peace treaty and an end to decades of economic sanctions.

“The promise is they wouldn’t be shooting off missiles in the meantime, and they’re looking to de-nuke,” Mr. Trump shouted to reporters on the way to a rally in the Pittsburgh area on Saturday.

The “promise” he referred to was conveyed by South Korea’s national security adviser; so far Mr. Kim has made no such commitment in public, nor agreed that American military exercises with the South can proceed, another of the conditions that the White House says the North has volunteered.