Pompeo says that US sanctions on the North will remain in place until the North denuclearizes.
The Secretary added that if diplomatic efforts fail, then pressure on Pyongyang will increase.
U.S. President Donald Trump and North Korean leader Kim Jong-un may strike a "deal of the century" today in Singapore.
It wasn't immediately clear what specific progress, if any, had been made in preliminary discussions between US and North Korean officials in the run-up to the Tuesday summit.
Mr Trump and Mr Kim arrived in Singapore on Sunday, both staying at luxurious and heavily guarded hotels less than one kilometre, with Mr Trump at the Shangri-La Hotel and Mr Kim at the St Regis Hotel.
Seoul does believe, they added, that it will be possible to achieve the goal "at any time" if a favorable environment emerges from the DPRK-U.S. summit.More news: Vladimir Putin invites Kim Jong Un to Russian Federation in September
"I think the minimum would be a relationship".
Imagine if President George W. Bush had met Iraqi leader Saddam Hussein for face-to-face negotiations in January 2003 in Egypt instead of the USA -led invasion going ahead two months later and you get a sense of how remarkable this summit is.
Trump also tweeted: "Meetings between staffs and representatives are going well and quickly. but in the end, that doesn't matter".
Trump spoke only briefly in public on Monday, forecasting a "nice" outcome.
Meanwhile, Law and Home Affairs Minister Shanmugam is confident that security is in place for the Trump-Kim summit.
Pyongyang has said it is willing to deal away its entire nuclear arsenal if the U.S. provides it with reliable security assurances and other benefits.
United States and North Korean officials were still meeting on the eve of the summit in an effort to bridge the gap between the two countries on how to substantively achieve North Korean denuclearization.More news: Comcast makes $65 billion offer for Fox, setting up brawl
Monday saw the Blue House official say the "very significant meaning" Kim-Trump meeting would be if the two confirmed each other as "credible partners".
Meanwhile, diplomats from the U.S. and North Korea met behind closed doors at The Ritz-Carlton hotel, in a bid to narrow their differences ahead of the Trump-Kim summit tomorrow.
While US officials are hopeful that Kim is prepared to take North Korea in a new direction by agreeing to denuclearization, Kim remains a ruthless dictator who has committed slews of human rights violations, ordered family members executed and spent millions of dollars advancing his nuclear and ballistic missile programs while his people face food shortages and poverty.
But in the lead up to the historic summit, several analysts have pointed out that the Trump administration doesn't have a clear plan for how it will approach the discussions, and that both sides of the negotiating table have very different ideas about what "denuclearization" means. That's according to South Korea's presidential office of Cheong Wa Dae at a press briefing in Singapore on Monday.
Trump said, "We've got a very interesting meeting, in particular, tomorrow, and I think things can work out very nicely".
During his news conference, Trump said that Kim told him he would soon destroy a nuclear test site.
The selfie sees Kim offer a wholesome smile, a display that belies the iron-fist with which he rules over North Korea.More news: Donald Trump confident of 'terrific relationship' with Kim Jong Un
Among the three dozen or so North Koreans seen at breakfast on Monday were some of the regime's most powerful men, usually only spotted by North Korea watchers in photographs published in state media as they line up at official events.