"Major disarmament... We're hopeful that we can achieve that in the two and half years", he said, adding that there is "a lot of work left to do".
To which Trump said: "Yeah, but so have a lot of other people done some really bad things".
Another 26 percent said they believed the United States and North Korea would meet their commitments, while 34 percent said they did not know whether they would follow through. He and Mr Trump met on a red carpet in front of a backdrop of equal numbers of U.S. and North Korean flags at the Capella hotel, a luxury resort on Singapore's Sentosa Island.
Trump has made it a habit to attack the free press in tweets when the narrative shared by numerous reporters doesn't match his own views of an event.
Mr Kim was on his way to visit Marina Bay Sands and Gardens by the Bay then. American officials said before the meeting they would insist that Mr Kim agree to the "complete, verifiable and irreversible dismantlement" of his nuclear weapons arsenal. That stood in contrast to the Trump administration's insistence that no sanctions relief will come until North Korea jettisons its entire nuclear program.
Despite hosting a press conference in Singapore for over 60 minutes with reporters, establishment media remained heavily critical of Trump's meeting with Kim.
Pompeo also sought to downplay Trump's announcement on Tuesday that military exercises with South Korea would be suspended in return for North Korea's denuclearization.
Pompeo, who is scheduled to travel to Beijing Thursday, said he isn't sure when the next conversation with North Korea will next take place but that it could happen "fairly quickly" - as soon as the coming week.
The agreement signed Tuesday by Trump and Kim also included provisions for future negotiations, hinting at the possibility of more meetings between the USA and North Korean leaders.
President Donald Trump challenged skeptical media coverage of his historic summit with North Korea's Kim Jong-un, declaring that "Fake News" is the nation's "biggest enemy". The latest example concerns North Korea.
Speaking in South Korea, where he discussed the outcome of the summit, Secretary Pompeo said there was still "a great deal of work to do" with North Korea.
Still, some Korea watchers said that it was better for the United States and North Korea to be talking than threatening each other, even without a host of specific commitments from Mr Kim.
Greeting the South Korean delegation, An, the North's top delegate, joked that Kim would be recorded as the first person in uniform who has crossed the military demarcation line that divides the two Koreas. Trump cast the decision as a cost-saving measure, but also called the exercises "inappropriate" while talks continue.
The traditional USA calendar for other major drills would not pick up again until next spring, officials say. The next scheduled major exercise, involving tens of thousands of troops, normally would be held in August. He said he planned to continue sharing the view with Washington and Seoul.
Kim, Trump in countdown to historic summit
Singapore is one of the few countries which shares cordial relations with both United States and North Korea. That according to a senior official in President Donald Trump's administration.