US President Donald Trump says he had "a long and very good talk" with the South Korean president, Moon Jae In, after his historic meeting with North Korean leader Kim Jong Un.

With anticipation growing for a possible US-North Korea summit, Trump tweeted that "things are going very well", with the "time and location" of a meeting with Kim Jong Un still being set.

The call lasted 75 minutes, according to a statement from the South Korean president's office quoted by the news agency Yonhap.

Trump said he also spoke by phone with Japanese Prime Minister Shinzo Abe "to inform him of the ongoing negotiations", and the Pentagon said US Secretary of Defense James Mattis spoke with South Korean Defence Minister Song Young-moo.

Moon and Kim have pledged to seek a formal end to the Korean War by the end of the year and to rid the Korean Peninsula of nuclear weapons.