U.S. Secretary of State Mike Pompeo said in an interview aired on Sunday that he told North Korean leader Kim Jong-un that he will have to agree to take "irreversible" steps toward shutting his nuclear weapons program in any deal with U.S. President Donald Trump.

"We use the word 'irreversible' with great intention," Pompeo told ABC News. "We are going to require those steps that demonstrate that denuclearization is going to be achieved."

Pompeo's comments were the most extensive yet regarding his Easter weekend talks in Pyongyang with Kim in preparation for a summit as early as next month between the North Korean leader and Trump.

Pompeo, the former CIA director who was sworn in as the top U.S. diplomat on Thursday, said his meeting with Kim was "a productive one" and that he left Pyongyang convinced there is "a real opportunity" for the North Korean leader and Trump to strike a deal.

Kim expressed his readiness to discuss Trump's demand "and to lay out a map that will help us achieve that objective," Pompeo said.

His assessment likely will add to hopes for a breakthrough that brings peace to the divided Korean peninsula following a historic summit last week between Kim and South Korean President Moon Jae-in at which the pair vowed "complete denuclearization."

Seeking concrete measures

While Pyongyang says it will close its nuclear test site next month, Kim and Moon did not outline concrete measures to be taken to achieve that goal of denuclearization.

Pompeo made clear that Trump will be seeking Kim's commitment to such steps, and added that the United States will also take matching actions, without providing details.

Pompeo however cautioned that "there remains a great deal of work to do." And he noted that previous North Korean promises "proved false or unworthy or they were incapable of keeping them."

"Both countries will have to do more than words," said Pompeo. He repeated that Trump will maintain a "pressure campaign" of harsh sanctions on impoverished North Korea until Kim shutters his nuclear weapons program.

He said that at Trump's direction, he spoke with Kim about the release of three U.S. citizens detained by North Korea. He did not elaborate on the outcome of that discussion.

Concern over Iran

Pompeo was interviewed remotely from the Middle East, where he is on a brief diplomatic tour. He met with Saudi King Salman in Riyadh on Sunday and stressed the need for unity among Gulf allies as Washington aims to muster support for new sanctions against Iran.

After meeting Israeli Prime Minister Benjamin Netanyahu later in the day, he said the United States is deeply concerned by Iran's "destabilizing and malign activities."

"We remain deeply concerned about Iran's dangerous escalation of threats towards Israel and the region," he said, speaking alongside the Israeli leader.

Pompeo's whilrwind trip began with a visit to NATO headquarters in Brussels on Friday, hours after he was confirmed as Trump's top diplomat. He has not even visited his own office yet, he told Netanyahu.