Mr Pompeo said the United States was prepared to walk away from the talks and a "bad deal" was not an option.
"A bad deal is not an option", Pompeo said in his written opening statement for a House of Representatives Foreign Affairs Committee hearing.
Mr Trump stunned the world when he confirmed that he and North Korean leader Kim Jong-un would be meeting for talks following a agreement apparently brokered by South Korean President Moon Jae-in.
Pompeo's reformulation of the USA demands was presaged by Trump on Tuesday, when a reporter asked if Kim could be expected to give up his nuclear capabilities all at once. Maybe it will happen at a different time.
The spat between the U.S. and North Korea over what denuclearisation means raised questions about how clear Pompeo had been in his two meetings with Kim at Easter and earlier this month. "The American people are counting on us to get this right".
Many observers had argued before Mr Trump met Mr Moon that there was too much at stake for Washington and Pyongyang not to proceed with the Singapore summit.
North Korea conducted several nuclear tests over the past few years and developed long-distance missiles which, it says, can carry nuclear bombs as far as the U.S. mainland.
North Korea must disarm before any economic relief, says Mike Pompeo
The United States and South Korea are working to keep the scheduled US summit with North Korea on track - even after President Donald Trump's comment that "there's a very substantial chance" it won't go off as planned.
However, based on his own discussions with the North Korean leader, Pompeo said he was hopeful that Trump could convince Kim to make a strategic decision to denuclearize.
The entire talk about North Korea wanting to cancel the summit started when scheduled talks between the North and South were canceled because South Korean military held joint exercises with the U.S. military.
It has said in previous, failed talks that it could consider giving up its arsenal if the United States provided security guarantees by removing its troops from South Korea and withdrew its so-called nuclear umbrella of deterrence from South Korea and Japan.
Pompeo says previous USA administrations had been "fooled before and we can't permit that to happen again". Trump didn't discuss all the conditions they have prepared for the North but was adamant that "denuclearisation must take place".
Mr Trump accepted North Korea's invitation for direct talks after more than a year of heated rhetoric and with global concern that hostilities might escalate into military confrontation.
Russian Federation announced Wednesday that Foreign Minister Sergei Lavrov will travel to North Korea for a visit on May 31.
Malaysian Pro-Democracy Leader Released From Detention
A popular Islamic student leader, Anwar joined the ruling Malay party in 1982, a year after Mahathir became prime minister. He reiterated his full support for Mahathir's leadership and said their political feud has always been buried.