SEOUL, South Korea — Kim Jong-un, North Korea’s leader, told South Korea’s president on Wednesday that he would commit to some concrete steps toward denuclearization — including an offer to “permanently dismantle” facilities central to fuel production for nuclear warheads. But he made no promises to relinquish his nuclear weapons or missiles.

Mr. Kim’s commitments fell far short of what American officials have demanded — a complete abandonment of the North’s nuclear and missile programs. Nonetheless, President Trump welcomed the agreements, reached during Mr. Kim’s summit meeting in North Korea with President Moon Jae-in of South Korea, as “very exciting.”

Speaking on the South Lawn of the White House, Mr. Trump told reporters that when he came into office “people thought we were going — it was inevitable — we were going to war with North Korea.”

Despite Mr. Trump’s insistence that he remained tough on North Korea, three outcomes from the meeting between Mr. Moon and Mr. Kim suggested the White House had softened its position.