Donald Trump and North Korean leader Kim Jong-un will meet June 12 in Singapore, the U.S. president announced Friday, a week after axing the planned meeting. 

After meeting for roughly two hours with Kim Jong-un's second-in-command at the White House, Trump said the meeting would be the start of "a process" aimed at achieving the denuclearization of the Korean Peninsula. 

“I think we would be making a big mistake if we didn’t have it,” Trump told reporters at the White House. "We're going to deal."

He met a North Korean delegation led by North Korean Vice Chairman Kim Yong-chol in the Oval Office for what was supposed to be a presentation of a letter the North Korean leader penned to Trump, but which was expanded to a more robust discussion.   

After saying the letter was "very nice" and "very interesting", Trump acknowledged he had not opened it before addressing reporters. 

Trump called off the June 12 summit last Thursday in a letter addressed to Kim, the North Korean leader, questioning the North's sincerity amid a series of tit-for-tat exchanges between Pyongyang and Washington. 

But in remarks to reporters this Friday, Trump said he now thinks the meeting will start a probably "very successful" process. 

Asked if he thought the North Koreans were willing to denuclearize, Trump said: "I think they want to do that. I know they want to do that. They want other things along the line. They want to develop as a country. That's going to happen. I have no doubt."

In addition to denuclearization, Trump said the U.S. and North Korea will discuss a formal end to the decades-old Korean War, and human rights -- a topic, he acknowledged, was not broached during Friday's two-hour sit-down -- when he meets Kim in Singapore. 

The U.S. and North Korea have had teams in the DMZ between the North and South, Singapore and the U.S. this week working to iron out the details ahead of the summit. 

Kim Yong-chol had been meeting with Secretary of State Mike Pompeo in New York since Wednesday before departing for Washington. He is the highest ranking North Korean official to step foot outside of a diplomatic zone around the UN's New York headquarters in decades. In order to do so, he had to receive special authorization. 

Pompeo became the highest ranking official to meet Kim Jong-un when they met in North Korea in April when the former was leading the CIA.