Trump says peace on the Korean peninsula 'looks like it could happen' The president says he defied what people called an "impossibility."

The day that North and South Korea declared a shared goal to denuclearize the peninsula and end the Korean War, President Donald Trump confirmed that a hope for the people of North and South Korea to “someday live in harmony, prosperity and peace” now "looks like it could happen."

“When I began people were saying that was an impossibility. They said there were two alternatives, let them have what they have or go to war. And now we have a much better alternative than anyone thought possible,” Trump said during a White House ceremony honoring the U.S. Olympic and Paralympic teams.

The president also described a hopeful future in which future Olympians could compete on a denuclearized peninsula.

“Hopefully the day will come, when Olympic athletes can compete on a Korean peninsula that is free of nuclear weapons and where all Koreans can live together and share their dreams, it would be a wonderful thing to do,” Trump said.

Friday marked the end of a historic summit between President Moon Jae In of South Korea and Kim Jong Un, the leader of North Korea.

It was the first time since 2007 leaders of the two countries have met, but the summit had been in the works for some time. There were two previous meetings between high-level officials from the North and South, as well as the North's participation in the Winter Olympics in Pyeongchang, South Korea, earlier this year. The two nations marched under one flag.

The president is now gearing up for a potential meeting with Kim by May or June. In the lead-up to that meeting, then-CIA Director but now-confirmed Secretary of State Mike Pompeo North Korean leader quietly traveled to North Korea to meet with Kim over Easter weekend.

Great to have Secretary Pompeo confirmed. He will do an excellent job helping @POTUS lead our efforts to denuclearize the Korean Peninsula. (photos from previously confirmed Easter weekend trip) pic.twitter.com/o4RNDKVmah

On Friday morning, the president tweeted that Americans should be "very proud" of "what is now taking place in Korea," referring to the inter-Korean summit. Cautiously optimistic, he also tweeted, “Good things are happening, but only time will tell!"

The president then tweeted about the role Xi Jinping, China's president, had in the negotiations. Xi met secretly with North Korea's Kim Jong Un in Beijing late last month.

The meeting was the first time a North Korean leader had ever set foot in the South.

"We talked about peace and prosperity," South Korean president, Moon Jae In, said. "A bold decision has been made. Big applause should be given to Kim Jong Un."

"There is no turning back," he added.

Kim, who took over as North Korean leader after his father’s death in 2011, was also positive.

"Same people, same blood, so we cannot be separated and should live together in unification," Kim said. "I hope we live together soon as a new path forward."

The president’s tweets Friday are starkly different from past comments he's made about Kim.

Last year he tweeted that he had a “nuclear button” that’s “much bigger and more powerful” than Kim’s, and announced that the U.S. was “locked and loaded” should North Korea “act unwisely.” Trump repeatedly referred to Kim in his tweets as “Little Rocket Man.”

But Trump has been resolute in his goal to denuclearize the peninsula.

“When I came into office, people thought we were going into nuclear war, OK, and now they're saying wow — it looks like that's going to be taken care,” Trump said Thursday on "Fox & Friends."

The U.S. and North Korea have narrowed down the location of a meeting to five locations. A senior U.S. official previously told ABC News that Trump had ruled out China and that it was highly unlikely Kim would agree to meet in the U.S. or that Trump would agree to a location in North Korea.

Possible venues include Sweden or Switzerland.

Joohee Cho and Hakyung Kate Lee contributed to this report.