President Donald Trump and Defense Secretary Jim Mattis spoke on Saturday with their South Korean counterparts after the historic meeting between leaders of the two Koreas, and Trump said "things are going very well" as he prepares for an expected summit with the North's Kim Jong Un.

Mattis and Defense Minister Song Young-moo said they were committed to "a diplomatic resolution that achieves complete, verifiable and irreversible denuclearization" of the North, according to the Pentagon's chief spokeswoman, Dana W. White. Mattis also reaffirmed "the ironclad US commitment" to defend its ally "using the full spectrum of US capabilities".

Trump tweeted Saturday that he had "a long and very good talk" with President Moon Jae-in. He also said he updated Japan's prime minister, Shinzo Abe, about "the ongoing negotiations" for an anticipated summit with Kim, tentatively scheduled for May or early June.

Moon and Kim have pledged to seek a formal end to the Korean War, fought from 1950 to 1953, by the year's end, and to rid the Korean Peninsula of nuclear weapons. Trump has said he's looking forward to the meeting with Kim and that it "should be quite something."

"Things are going very well, time and location of meeting with North Korea is being set," Trump tweeted.

Trump is claiming credit for the Korean summit, but now faces a burden in helping turn the Korean leaders' bold but vague vision for peace into reality after more than six decades of hostility.