Secretary of State Mike Pompeo met Thursday with North Korea's former military intelligence chief to continue discussions aimed at salvaging a scrapped meeting between President Donald Trump and North Korean leader Kim Jong Un.

Pompeo met with Kim Yong Chol, described by NPR as "Kim Jong Un's right-hand man," Thursday morning in New York City after the pair started discussions over dinner one night earlier.

Pompeo said after the meeting that Thursday’s discussion was “substantive” and that “good progress” had been made toward re-establishing the planned June 12 meeting in Singapore.

"We discussed our priorities for the potential summit between our leaders," he wrote. "#NorthKorea and the world would benefit greatly from the denuclearization of the Korean Peninsula."

Trump said Thursday morning that officials were having “very good meetings with North Korea.”

“I believe they will be coming down to Washington on Friday (with) a letter being delivered to me from Kim Jong Un,” he told reporters gathered at Join Base Andrews. “It is very important to them.”

He said he still hopes that North Korean and U.S. officials can meet next month despite his decision last week to cancel the summit amid tension with North Korea.

"I think it will be very positive,” Trump said of Thursday’s discussions. “We will see what happens. It is all a process."

Two other meetings related to the planned summit also took place Thursday, according to The Washington Post. A U.S. delegation was meeting Thursday with North Korean officials in the demilitarized zone between North and South Korea. In Singapore, officials from both countries met to discuss logistics.

If the summit takes place, it will be a historic meeting between the two nations.

Trump on May 24 abruptly canceled the summit in a letter addressed to Kim Jong Un, citing the country’s “tremendous anger and open hostility.” However, he didn’t dismiss the possibility that the meeting could be rescheduled. North Korean officials also said they'd still be willing to meet face-to-face, despite the tension.

WATCH: Trump Speaks on Canceled N. Korea Summit