Trump: No More Nuclear Threat from North KoreaU.S. President Donald Trump declared Wednesday, "There is no longer a Nuclear Threat from North Korea," as he returned home from a summit in Singapore with North Korean leader Kim Jong Un. "Just landed - a long trip, but everybody can now feel much safer than the day I took office," Trump wrote on Twitter. "Meeting with Kim Jong Un was an interesting and very positive experience. North Korea has great potential for the future!" Kim agreed Tuesday "to complete denuclearization of the Korean Peninsula" during the summit, while Trump unexpectedly said he was suspending military drills with South Korea. Trump on Wednesday said "We save a fortune by not doing war games, as long as we are negotiating in good faith - which both sides are!" The document the two leaders signed 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. No specifics \n\nCritics 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. Trump has defended the agreement as a major step in dealing with the threat of nuclear-armed North Korea and said he believed Kim's government would start the process of living up to the agreement right away. "Before taking office people were assuming that we were going to War with North Korea," he tweeted Wednesday. "President Obama said that North Korea was our biggest and most dangerous problem. No longer - sleep well tonight!" 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. 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. Respond in kind \n\nKim 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 agreement 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. "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: Trump on US troops in S. Korea No media source currently available A Pentagon spokesman said Defense Secretary Jim Mattis was "not surprised" by Trump's concession ending the military exercises 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." Optimistic tone \n\nTrump 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. WATCH: Trump on human rights No media source currently available 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. "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." White House invite \n\nTrump 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.\n\nBill Gallo contributed to this report