NEW YORK/SEOUL -- U.S. President Donald Trump said on Sunday that negotiators have entered North Korea to prepare for the summit between himself and leader Kim Jong Un, a meeting he abruptly canceled on Thursday.

"Our United States team has arrived in North Korea to make arrangements for the Summit between Kim Jong Un and myself," the president tweeted on Sunday afternoon. "I truly believe North Korea has brilliant potential and will be a great economic and financial Nation one day."

He went on to say: "Kim Jong Un agrees with me on this. It will happen!" -- the most positive comments on the prospects for the meeting, originally planned for June 12 in Singapore.

The American delegation is headed by Sung Kim, a former U.S. ambassador to South Korea, accompanied by Pentagon official Randall Schriver, Reuters reported. They were to meet with North Korean Vice Foreign Minister Choe Son Hui, whose fiery "nuclear-to-nuclear showdown" statement days earlier triggered Trump to cancel the Singapore summit.

The Washington Post reported that the talks at the border would continue on Monday and Tuesday at Tongilgak, a North Korean building in the truce village of Panmunjom, which separates the two Koreas.

South Korea President Moon Jae-in said on Sunday that the North's Kim is ready to accept American demands for complete, verifiable and irreversible denuclearization and that he has the strong will necessary to follow through with the complete denuclearization of the Korean Peninsula.

He also said Kim told him he wants the U.S. to provide a security guarantee in exchange for the North's follow-through.

Sung Kim addresses the media as U.S. special representative for North Korea policy in Beijing in April 2016. © Reuters

Moon met with Kim on Saturday at Kim's request in Panmunjom, where the two leaders exchanged views on the denuclearization process as well as Kim's possible summit with Trump. Moon said Kim requested the meeting to help resolve issues between the two Koreas and to pave the way for the success of his summit with Trump.

"Chairman Kim Jong Un expressed his will for the complete denuclearization on the Korean Peninsula clearly again, after he did so in the Panmunjom Declaration," Moon said in a press briefing. "He showed his intention to cooperate for peace and prosperity as well as end the history of war and conflicts through the success of the North Korea-U.S. summit."

Asked whether Kim is willing to accept the conditions suggested by Washington, Moon said it is his understanding that the U.S. may have already established it. "I think the U.S. may have confirmed North Korea's will for this," he said. "If there is something unresolved, I think [the Americans] could confirm this during their working-level negotiations."

Moon said Kim worries that the U.S. will remain hostile toward North Korea and wants it to guarantee the security of his country if Pyongyang gives up its nuclear and missile programs. Moon said he told Kim that Trump expressed his will to help North Korea prosper economically as well as end hostile relations when the North follows through on denuclearization.

Just before Moon's news conference on Sunday, Trump said at the White House that he is still considering meeting with Kim on June 12 in Singapore as originally planned. "That hasn't changed," he told reporters.

The North's official Korean Central News Agency reported on Sunday that Kim expressed his "fixed will" on the historic summit with the U.S. leader.

Jin Chang-soo, president of the Sejong Institute in Seongnam, said the chances of a Trump-Kim summit are very high, since it would help both leaders. He said it is important to see the process from the perspective of interests instead of focusing on rhetoric.

"For Kim Jong Un, the dialogue mode will lead to a softening of international sanctions on North Korea," Jin said. "That is also good for Trump, who can use this momentum for the domestic politics."

"Unlike power elites in Washington who distrust North Korea's will [to follow through on American demands], the leaders of the two countries have common political interests for the summit," he said.