North Korea has been developing nuclear-tipped missiles capable of reaching the U.S. mainland, which has prompted an escalating war of words between Mr Trump and North Korean leader Kim Jong-un, which often relied on threats of war.
He made the remarks during a meeting with South Korean President Moon Jae-in, who is eager to engage the North after one of the most hostile periods in recent years on the Korean Peninsula.
Fireworks and ice marked the end of the Winter Olympics Sunday in Pyeongchang, North Korea.
During the closing ceremony, Ivanka Trump and the USA delegation congratulated Moon and the First Lady "on an incredible Olympic Games and applauded throughout the ceremonies, including for the US and South Korean Athletes", the administration official said in a statement.
Trump and Kim sat close to each other in the VIP area.
The delegation took a different route, prompting the opposition Korea Liberty Party to accuse President Moon Jae-in's administration of "abuse of power and an act of treason" by re-routing the motorcade to shield it from the protest.
The visit by Kim Yong Chol, who led an eight-member high-level delegation that crossed the Demilitarized Zone in the morning, is the final piece of the games-led diplomacy that has dominated headlines from Pyeongchang.
Choe Kang Il, a senior North Korean diplomat handling affairs with the United States, was also part of the delegation, South Korea's Yonhap news agency reported, citing Seoul officials.
Hooker was seen accompanying Ivanka Trump at the airport. The US delegation arrived Friday for a four-day visit.
Also part of the US delegation was Allison Hooker, a National Security Council adviser for Korean issues.
North Korea has denied its involvement in the sinking.
North Korea and the USA, however, had each dismissed the possibility of any interaction between their officials.
Moon met Kim for about an hour beginning 5pm in Pyeongchang, the presidential office said without elaborating.
"We will see if Pyongyang's message today, that it is willing to hold talks, represents the first steps along the path to denuclearization", the statement read.
Donald Trump has warned of a new phase in the U.S. strategy to pressure the North Korean regime into giving up its nuclear programme.
This development came after the U.S. President Donald Trump on Friday announced new sanctions on North Korea, specifically targeting the country's shipping and trading companies to further isolate the communist country economically.
China also reacted angrily to the new USA measures, saying on Saturday the unilateral targeting of Chinese firms and people risked harming cooperation on North Korea. Add North Korea as an interest to stay up to date on the latest North Korea news, video, and analysis from ABC News.
Trump also warned that, if the latest sanctions do not work, the United States may "go to phase two" that "may be a very rough thing".
Trump, it said, should know that the North would "have no dealings with those viciously slandering the dignity of our supreme leadership and government".
In response, Pyongyang blasted Washington for heightening the possibility of "confrontation and war" on the Korean Peninsula.
Pyongyang's foreign ministry praised the way the two Koreas had co-operated together during the Olympics, but said the United States had "brought the threat of war to the Korean peninsula with large-scale new sanctions" just as the Games were coming to a close.