U.S. President Donald Trump defended his agreement with North Korean leader Kim Jong Un, saying the world "has taken a big step back from potential nuclear disaster."
Kim agreed Tuesday "to complete denuclearization of the Korean Peninsula" during the historic summit between the two leaders in Singapore, while Trump unexpectedly said he was suspending military drills with South Korea.
"No more rocket launches, nuclear testing or research!" Trump wrote on Twitter. "The hostages are back home with their families. Thank you to Chairman Kim, our day together was historic!"
North Korea's official news agency on Wednesday quoted Kim as saying it is "urgent" that both North Korea and the United States "make a bold decision on halting irritating and hostile military actions against each other," while mentioning Trump's pledge to halt the military exercises.
Kim said if the United States takes "genuine measures for building trust," he would take "additional goodwill measures of next stage commensurate with them." No details of what those steps would be were given.
The report also mentioned that Kim invited Trump to Pyongyang while Trump invited him to Washington and said both accepted the other's invitation as "another important occasion for improved relations."
The document the two leaders signed Tuesday did not include details of how and when North Korea would denuclearize, nor did it spell out exactly what "security guarantees" the United States would provide to North Korea.
It calls for the two countries to jointly work on efforts to build a lasting peace on the Korean Peninsula, to establish new U.S.-North Korea relations and to recover the remains of prisoners of war and military members missing in action. The two sides promised to hold follow-up negotiations.
'Denuke North Korea'
Critics pointed to the lack of specifics in the agreement while questioning whether Trump gave up too much while securing too little in return during his several hours of talks with Kim in what was the first meeting between a sitting U.S. president and a North Korean leader.
Despite no timeline in the agreement, Trump said at a news conference, "We're starting that process very quickly," and expressed confidence Kim's government would start the process right away.
Former U.S. ambassador Bill Richardson told VOA he is concerned about no verification of what the North Koreans will do about missile technology in the DPRK, no detail of nuclear reduction, the peace treaty and human rights.
Trump used Twitter posts to reject criticisms and say "great progress was made on the denuclearization of North Korea."
"A year ago the pundits & talking heads, people that couldn’t do the job before, were begging for conciliation and peace - 'please meet, don’t go to war.' Now that we meet and have a great relationship with Kim Jong Un, the same haters shout out, 'you shouldn’t meet, do not meet!'"
"We're going to denuke North Korea," Trump told VOA contributor Greta Van Susteren, adding that U.S. troops stationed in South Korea will remain in place, but announcing one concession long-sought by North Korea was included in the document signed earlier in the day.
"We are going to get out of the war games that cost so much money," he said referring to the U.S. participation in joint military exercises with South Korea. At his news conference, Trump said the war games were expensive, provocative and inappropriate.
WATCH: US-S. Korea joint military exercises
Later, a Pentagon spokesman said Defense Secretary Jim Mattis was "not surprised" by Trump's concession ending the war games and had been consulted, including discussions with Trump and Secretary of State Mike Pompeo.
"We welcome the outcomes," the defense spokesman said. "We support them."
Sanctions will stay — for now
Trump struck an optimistic tone about his talks with Kim. "My meeting with Chairman Kim was honest, direct and productive. We got to know each other well in a very confined period of time," he said.
The U.S. leader stressed that existing U.S. sanctions will remain in place until North Korean nuclear weapons "are no longer a factor."
On human rights, Trump said Tuesday's meetings only very briefly touched on the topic but that the two sides would discuss it more in the future. When asked about thousands of people imprisoned in labor camps, Trump said he thinks he has helped them because things in North Korea will change.
"I think they are one of the great winners today," he said.
He cited American college student Otto Warmbier, who was arrested by North Korean authorities in 2016 and died a year ago after being repatriated to the United States with severe brain damage.
WATCH: Human rights
"Otto did not die in vain. He had a lot to do with us being here today," Trump said.
Hours earlier as he sat alongside Kim at the signing ceremony, Trump said the two leaders "have developed a special bond" and that after their several hours of talks Tuesday and the signing of the agreement, he thinks the U.S. relationship with North Korea "will be very different than in the past."
Trump said he would "absolutely" invite Kim to visit the White House and is open to visiting Pyongyang, as well.
"Today, we had a historic meeting and decided to leave the past behind," Kim said, speaking through a translator. "The world will see a major change."
Kim at one point told Trump that many people around the world would see their meeting as a kind of fantasy, as if it the event was a "science fiction movie."
They first met Tuesday for about 40 minutes alone, except for their translators, before bringing in delegations from their respective sides for a working lunch. They walked outside together after the lunch, stopping briefly to look at the U.S. president's special limousine.
Bill Gallo contributed to this report in Singapore.