(CNN) A letter was delivered from US President Donald Trump to North Korean leader Kim Jong Un over the weekend, a source familiar with the ongoing denuclearization talks between Washington and Pyongyang told CNN.

The letter comes as the two sides negotiate details of a second meeting between the two leaders. It was flown to Pyongyang and delivered by hand, the source said.

According to the source, North Korea's former spy chief Kim Yong Chol -- one of Pyongyang's top negotiators -- could visit Washington as soon as this week to finalize details of the upcoming summit.

CNN previously reported that US scouting teams had visited Bangkok, Hanoi and Hawaii as they search for a location for the second summit.

Last week, South Korean President Moon Jae-in threw his support behind another Trump-Kim meeting , saying it -- along with a visit by Kim to Seoul -- would be a turning point "that will firmly solidify peace on the Korean Peninsula."

"We will not loosen our guard until the promise to denuclearize the Peninsula is kept, and peace is fully institutionalized," Moon added.

New summits

After years of isolation, Kim held a number of diplomatic summits in 2018, meeting with Moon, Trump and Chinese President Xi Jinping. Events so far suggest 2019 could be similarly busy.

Last week, he made a surprise visit to Beijing to meet again with Xi , a meeting which served to emphasize that not only does Pyongyang have partners beyond Seoul and Washington, but also that China remains a major player in any future action to denuclearize the Korean Peninsula.

According to a statement from Chinese state-run news agency Xinhua, Xi and Kim agreed to "constantly advance the political settlement process of the Korean Peninsula issue."

North Korean state media gave a little more away, saying Kim shared his concerns about potential obstacles to the future growth of US-North Korean relations, and Xi "completely sympathizes that the reasonable points of interest of North Korea deserve to be resolved."

Last year, North Korea "heightened its international influence and it had received a great support, understanding, and fervent welcome from the whole world," KCNA noted.

Kim had been due to visit the South Korean capital in December, but that summit was repeatedly delayed as the denuclearization process and talks between Pyongyang and Washington ran into difficulties.

Responding to a question about the visit at a press conference last week, Moon said he'd received a "special" letter from Kim in December explaining why he couldn't visit the South last year but saying he wanted to see the South Korean leader more often.

"Our reunion in Pyongyang feels as if it happened yesterday but it has already been almost 100 days and the unforgettable year 2018 is drawing to an end," Kim said in the letter, an extract of which was shared by South Korea's Blue House.

While still Trump's biggest foreign policy success, the US President's first meeting with Kim was criticized by some for failing to hold North Korea to firm guarantees. Concerns have been raised since over Pyongyang's commitment to denuclearization and Washington's own willingness to take the steps needed for a peace treaty to be signed.

"Now I say this, North Korea, we're doing very well," Trump told reporters outside the White House last week . "And again, no rockets. There's no rockets. There's no anything. We're doing very well."

Trump noted that sanctions against North Korea will remain "in full force and effect" in the meantime, and warned that if anyone else had been elected US president, "you'd be at war right now."

"You would right now be in a nice, big fat war in Asia with North Korea if I wasn't elected president," Trump said.