President Trump said the logistics for his planned meeting with North Korean leader Kim Jong Un are “going very well” after speaking with South Korean President Moon Jae-in on Saturday.

The president said he spoke with the South Korean leader the day after Moon held a historic summit with Kim on Friday.

“Just had a long and very good talk with President Moon of South Korea,” Trump tweeted. “Things are going very well, time and location of meeting with North Korea is being set. Also spoke to Prime Minister [Shinzo] Abe of Japan to inform him of the ongoing negotiations.”

Moon and Kim met Friday at the border village of Panmunjom and vowed to remove nuclear weapons from the Korean Peninsula. However, they didn't identify specific, new measures to achieve that goal.

The summit was almost inconceivable a few months ago, after a year when the bordering countries seemed on the verge of war.

The Koreas, which have technically remained at war since the 1950-1953 Korean War was only stopped via an armistice, have agreed to stop all hostile acts over "land, sea and air" that can cause military tensions and clashes.

On Friday, Trump claimed credit for the historic inter-Korean summit, saying he has a responsibility to try and achieve peace and denuclearization.

"And if I can't do it, it'll be a very tough time for a lot of countries, and a lot of people. It's certainly something that I hope I can do for the world," he said.

World leaders hope Trump and Kim can perhaps further solidify or advance the Korean agreement if they indeed meet in May or June, as projected. However, they remain skeptical.

Abe on Friday praised the Korean talks as a "forward-looking move." He said he expects North Korea to take concrete actions toward denuclearization through its planned talks with the United States. Secretary of State Mike Pompeo recently met with Kim in North Korea, in advance of an upcoming summit.

The Japanese prime minister also said he hopes to get further details about the meeting between the Korean leaders and Moon's evaluation of the talks when they talk by phone.

A meeting between Trump and Kim also seemed impossible until recent weeks, amid North Korea’s recent testing of a nuclear warhead and ballistic missiles that could launch a nuclear weapon. Just four months ago, Kim threated the U.S. with nuclear weapons.

The tests resulted in stiff economic sanctions and an alarming exchange of public name-calling between Trump and Kim that sparked fear of war. Trump had called Kim “Little Rocket Man.” And Kim had called Trump a “dotard.”

The president pushed back against critics who say he's being manipulated by Kim, who has abruptly shifted to diplomacy after last year's full-scale push to become a nuclear power capable of threatening the U.S. mainland.

"I don't think he's ever had this enthusiasm for somebody, for them wanting to make a deal," Trump said in the Oval Office. "We're not going to be played, OK. We're going to hopefully make a deal. The United States in the past has been played like a fiddle."

The Associated Press contributed to this report.