A jet carrying Kim landed hours earlier.
"In light of how many flimsy agreements the United States has made in previous years, this president will ensure that no potential agreement will fail to ultimately address the North Korean threat", Pompeo told reporters in Singapore on Monday.
He and Trump are set to meet Tuesday morning in the first summit of its kind between a leader of North Korea and a sitting U.S. president. The North has faced crippling diplomatic and economic sanctions as it has advanced development of its nuclear and ballistic missile programs.
Trump is set to meet with Lee on Monday.
"It's the case in each of those two countries there are only two people that can make decisions of this magnitude and those two people are going to be sitting in the room together tomorrow", said Pompeo.
Shortly after 9 a.m. local time, Trump and Kim walked along a white colonnade, meeting in front of a bank of 12 alternating USA and North Korean flags where they shook hands.
However, he played down the possibility of a quick breakthrough and said the summit should set the framework for "the hard work that will follow", insisting that North Korea had to move toward complete, verifiable and irreversible denuclearisation. He also has sought to lower expectations for the meeting, saying it may be the start of a longer process. Pyongyang has advocated for decades for a peace treaty to formally end the Korean War, rather than the armistice that has been in place for more than 60 years. But some US officials have questioned whether Trump was doing enough to get up to speed.
He declined, however, to reveal any details of the preliminary discussions being held Monday between USA and North Korean officials.
Considering that both the North Korean leader and the USA president are expected to depart Singapore quickly after the summit, Rodman might be making the trip here for nothing after all.More news: Putin criticizes Trump over Iran nuclear deal
Trump arrived at the hotel after issuing a flurry of tweets dismissing skeptics of the meeting between US leaders and the rogue nuclear nation as "haters & losers".
Rodman has no official role in the diplomatic efforts between his country and North Korea, but he appears to be invested in promoting positive ties between Washington and Pyongyang.
A successful summit could also herald momentous changes in the security landscape of northeast Asia, in a similar way to how the fall of the Berlin Wall in 1989 changed Europe.
Trump is hoping to get Kim to agree to get rid of his nuclear weapons, though he has said it may take many more meetings to get to that point.
Trump advisers cast his actions as a show of strength before the Kim meeting.
Pompeo did say the United States is "prepared to take what will be security assurances that are different, unique that America has been willing to provide previously".
South Korea's Hankook Ilbo reported that Singapore recommended the St Regis, which hosted Chinese President Xi Jinping during his 2015 summit with Taiwanese President Ma Ying-jeou, because it can be easily secured.
The US president and the leader of DPRK are quite different people.