Pompeo's visit to South Korea included "detailed security discussions" with Seoul intelligence officials and a visit to an island near the border with the North, according to the U.S. military command in Korea.
Without providing proof for their claims, North Korea's state security ministry said the CIA and South Korea's National Intelligence Service were plotting "to hurt the supreme leadership" of North Korea.
North Korea alleged a bribe paid to a North Korean citizen was used to train him as a terrorist as well as other "accomplices," The Post reported.
In retaliation, North Korea is undertaking "counterterrorism measures of justice," a spokesman for North Korea intelligence said, South Korean news agency Yonhap reported.
Pyongyang said it has "exposed the criminal who had infiltrated our interior, with the intention of carrying out terrorism, using a biochemical substance against our supreme leader."
North Korea state security also said the suspect was stationed in Khabarovsk, Russia, in June 2014, when he was approached by CIA and NIS agents.
"Upon his repatriation, the [intelligence agencies] conspired with [the suspect] to carry out a bomb attack on our supreme leader, either during an event at the Kumsusan Palace of the Sun, or at a military parade," the statement read.
Ri Byong Ho, the North Korea head of intelligence, said the suspect was a "very important person" and that "there have already been more than 80 planned terrorist attacks" that have been foiled.
Neither the CIA nor the NIS has commented on the claims.
In February, North Korean nationals were implicated in the assassination of Kim's older half-brother Kim Jong Nam at an airport in Malaysia.
Pyongyang has denied any involvement, and Kuala Lumpur delivered the slain Kim's body to North Korea after negotiations.