Choe, who leads negotiations with the United States, said North Korea's intention to denuclearize has not changed, KCNA reported.
The North Korean first vice foreign minister also said the United States should "change its position," according to the report.
Choe's remarks come a week after Pompeo told CBS News nuclear talks with North Korea are likely to be "bumpy" and "challenging."
"It's gonna be bumpy. It's gonna be challenging...I hope that we get several more chances to have serious conversations about how we can move this process forward," the top U.S. diplomat had said.
Choe said negotiations are being made difficult by the United States.
"Our intention to denuclearize has not changed, and we will denuclearize in due time," Choe said. "But it will only be possible under the condition the United States changes its method of calculation, and re-establishes its position."
The North Korean diplomat also issued a warning to Washington of an "undesirable outcome" should the United States not agree to "North Korea's deadline."
Kim Jong Un gave the Trump administration until the year's end to break the current impasse in stalled nuclear talks.
On Tuesday, North Korea did not limit its condemnations to the United States.
State media slammed South Korea's main opposition conservatives for "destroying the destiny of the Korean people."
In the statement, North Korea credited Kim for the improvements in inter-Korea relations and blamed politicians of South Korea's Liberty Korea Party for criticizing the policies of the administration of South Korean President Moon Jae-in.
The conservatives recently clashed with rival party politicians in South Korea's parliament, when the ruling Democratic Party and three other parties agreed to fast-track four reform bills without LKP participation, Yonhap reported Monday.