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Pompeo made the statement during a news conference with the South Korean and Japanese foreign ministers in Seoul Thursday, 24 hours after North Korean leader Kim Jong Un touched down in Pyongyang, triumphant after his meeting with US President Donald Trump.
North Korean state media KCNA reported Wednesday that Trump had discussed lifting sanctions against Pyongyang during his talks with Kim in Singapore.
"The President of the US expressed the possibility of suspending the US - South Korea joint military exercises ... and, as progress is made from dialogue and negotiations, lifting sanctions against DPRK," state media said.
But Pompeo said Thursday that Trump had been very clear there would only be sanctions relief after "complete denuclearization."
"He has said this from the very beginning, he said it again to Chairman Kim and he said it in his press conference following his meeting with Chairman Kim," he told reporters.
Pompeo is on a tour of East Asia visiting with US allies and diplomatic partners to brief them on Trump's talks. From South Korea, he'll fly to China for meetings with top officials in Beijing later Thursday.
Canceling drills requires 'consultations': South Korea
However speaking opposite Secretary Pompeo on Thursday, South Korean Foreign Minister Kang Kyung-wha said decisions to suspend the exercises would "require consultations."
"This is an issue that involves the Korea-US alliance and this requires consultations between the military authorities of the two countries the Korea and the United States and it will be the case in the future as well," she told reporters.
It echoed comments made after Trump's Tuesday announcement, when South Korea's presidential office said they needed "to figure out president Trump's accurate meaning and intention."
Pompeo also met with South Korean President Moon Jae-in on Thursday, who again described the Trump-Kim summit as "very successful."
"There are various opinions about the meeting, but the most important thing is that the talks have made it possible for people around the world, including the people of the US, SK and Japan, to escape the threats of war, nuclear threats and the threats of long range missiles," Moon said in a statement.
Xi pushed Trump to suspend drills, source says
Following his talks with Japan and South Korea, Pompeo will head to Beijing to brief the Chinese government on Trump's meeting with Kim. He's due to meet with Foreign Minister Wang Yi before talks with President Xi Jinping at 9 p.m. local time (9 a.m. ET).
The source added Xi had multiple direct conversations with Trump about the topic before the US President met with Kim.
"If they end these exercises then people in South Korea will begin to question why are US troops even there?" Bonnie Glaser, director of the China Power Project at CSIS, told CNN.
But both the Japanese and South Korean foreign ministers were firm in their statements on Thursday that the US alliance was strong and US troops were there to stay.
"Secretary Pompeo and I reaffirm that the South Korean US alliance ... is robust as ever, that the US forces in Korea has played and will continue to play a crucial role for deterrence and peace and stability on the Korean Peninsula," Kang said.
CNN's Jake Kwon contributed to this article.