U.S President Donald Trump says the scheduled June 12 summit with North Korea in Singapore will go ahead.

The president spoke outside the White House after a top aide to Kim Jong-un met with him in the Oval Office on Friday to deliver a letter from the North Korean leader, as the two sides try to revive an on-again, off-again nuclear summit.

The president spoke to reporters after the meeting, saying that "I think it'll be a process."

"I never said it goes in one meeting; I think it's going to be a process. But the relationships are building and that's a very positive thing."

"They want it, we think it's important, and I think we would be making a big mistake if we didn't have it," Trump said.

The two countries, eyeing the first summit between the U.S. and the North after six decades of hostility, have also been holding negotiations in Singapore and the demilitarized zone between the two Koreas.

When asked Friday about the upcoming summit, Trump said he thinks it will be a "getting to know you meeting … plus."

Kim Yong-chol was greeted at the White House by chief of staff John Kelly and then whisked into the Oval Office. He is the most senior North Korean to visit the White House in 18 years, a highly symbolic sign of easing tensions after fears of war escalated amid North Korean nuclear and missile tests last year.

The contents of the letter were not immediately known.

Trump said the letter was "very nice" but offered little detail, saying at some point people may be able to see the contents.

"But really, this was a letter presentation that ended up being a two-hour conversation," he said, adding later in the press briefing that he hadn't actually opened it yet.

"I didn't open it in front of the director," Trump said.

He told reporters he thinks North Korea is committed to denuclearization. Friday's meeting didn't touch on human rights questions, the president said, but did talk about the possibility of ending the Korean war.

He also talked about the collaboration that's happening with countries like South Korea and Japan, saying that he also sees positive things happening around North Korea, with China.

Speaking in Kentucky, Republican Senate Majority Leader Mitch McConnell said he expected the North Koreans to make "every effort they can to get sanctions and other relief and give up as little as possible."

"For these situations to work, you have to not want the deal too much," McConnell said. "You fall in love with the deal and it's too important [to] you to get it, and the details become less significant, you could get snookered."

Kim's arrival in Washington — in a small caravan of SUVs from New York — came a day after Secretary of State Mike Pompeo declared that he was confident negotiations with Pyongyang were "moving in the right direction."

Pompeo spoke to reporters at a news conference in New York after meeting Thursday with Yong-chol. "Our two countries face a pivotal moment in our relationship, and it would be nothing short of tragic to let this opportunity go to waste."

U.S. President Donald Trump talks with Kim Yong-chol, former North Korean military intelligence chief and one of leader Kim Jong-un's closest aides, after their meeting in the Oval Office of the White House in Washington, Friday. (Andrew Harnik/AP Photo)

Pompeo, the former CIA chief who has travelled to North Korea and met with Kim Jong-un twice in the past two months, said he believed the country's leaders are "contemplating a path forward where they can make a strategic shift, one that their country has not been prepared to make before."

He tweeted from New York: "Good progress today during our meetings" with Kim and his team. Yet he also said at his news conference that difficult work remains including hurdles that may appear to be insurmountable as negotiations progress on the U.S. demand for North Korea's complete, verifiable and irreversible denuclearization.

"We will push forward to test the proposition that we can achieve that outcome," he said.

Pompeo spoke after meeting with Kim Yong-chol for a little more than two hours at the residence of the deputy U.S. ambassador to the United Nations. The talks had been expected to be held in two sessions, one in the morning and one in the early afternoon, and had not been expected to conclude until 1:30 p.m. Instead, the two men wrapped up at 11:25 a.m.

Pompeo said they finished everything they needed to address in the morning session. Immediately afterward, he tweeted that he had had substantive talks on the priorities for the potential summit. Pompeo was accompanied by Andrew Kim, the head of a CIA unit assigned to work on North Korea, and Mark Lambert, the head of the State Department's Korea desk.

Despite the upbeat messaging in the United States, Kim Jong-un, in a meeting with Russia's foreign minister on Thursday, complained about the U.S. trying to spread its influence in the region, a comment that may complicate the summit plans.

"As we move to adjust to the political situation in the face of U.S. hegemonism, I am willing to exchange detailed and in-depth opinions with your leadership and hope to do so moving forward," Kim told Sergey Lavrov.

North Korea's flurry of diplomatic activity following an increase in nuclear weapons and missile tests in 2017 suggests that Kim is eager for sanctions relief to build his economy and for the international legitimacy a summit with Trump would provide. But there are lingering doubts on whether he will ever fully relinquish his nuclear arsenal, which he may see as his only guarantee of survival in a region surrounded by enemies.

Trump views a summit as a legacy-defining opportunity to make a nuclear deal, but he has left the world guessing since cancelling the meeting last week in an open letter to Kim that complained of the North's "tremendous anger and open hostility." North Korea's conciliatory response to that letter appears to have put the summit back on track.

Mike Pompeo says the U.S. is moving forward, hoping for historic achievement. 0:34

Kim Yong-chol is the most senior North Korean visitor to the United States since Vice Marshal Jo Myong-rok visited Washington in 2000 to meet President Bill Clinton and Secretary of State Madeleine Albright. That was the last time the two sides, which are technically at war, attempted to arrange a leadership summit.

It was an effort that ultimately failed as Clinton's time in office ran out, and relations turned sour again after George W. Bush took office in early 2001 with a tough policy on the North.

Kim Yong-chol, vice chairman of the North Korean ruling party's central committee, was allowed into the United States despite being on a U.S. sanctions list, and North Korean officials are not normally allowed to travel outside the New York area.

The North Korean mission at the United Nations did not respond to an email seeking comment Thursday, and phone calls were not answered.

Koreas holding more talks

Meanwhile, the two Koreas agreed during a high-level meeting on Friday to hold talks later this month on military issues and reunions of families separated by the Korean War, a joint statement said.

The military talks will take place on June 14 on the northern side of the border village of Panmunjom in the demilitarized zone separating the two countries.

Talks about reunions of families separated by the 1950–53 war — which ended in a truce, not a peace treaty — would be held on June 22 at the Mount Kumgang resort north of the border, the statement said.