President Trump was introducing the pair at a gathering of Air Force personnel at Osan Air Base after travelling to South Korea form the north when he made the comparison. President Trump told mr Pompeo: “Mike, come up here Mike.” After calling him over the Republican addressed those travelling on the aircraft.
He said: “And you know who else we have here, Ivanka — alright come up Ivanka.”
Then, comparing the two, he added: “What a beautiful couple — Mike — Beauty and the Beast.”
His daughter and Mr Pompeo then strode to the podium.
Hours before, President Trump visited Kim in North Korea.
The American became the first sitting US president to set foot on North Korean soil when he met with the leader.
The two leaders met at the border of the Demilitarised area separating the north and south.
The meeting came eight weeks after the North demanded Mr Pompeo be left out of peace talks after accusing the diplomat of “reckless remarks” and “sophistry” after he claimed sanctions on the reclusive nation was bringing Pyontang to its knees.
Mr Trump tweeted an invitation to the North Korean leader for the meeting during the G20 Summit.
South Korean President Moon Jae-in confirmed Kim had accepted the invitation.
The US President asked Kim via Twitter to “say hello” and “shake his hand” at the border in an attempt to resolve the ongoing dispute over the rogue nation’s nuclear weapons programme.
Mr Trump told the press conference that he and Kim had “developed a very good relationship” and were looking forward to meeting.
Mr Moon praised Mr Trump and Kim for “being so brave”.
He said: “I hope President Trump will go down in history as the president who achieves peace on Korean Peninsula.”
President Trump has said he had “no problem” with crossing into North Korea.
Mr Trump arrived in South Korea on Saturday evening after meeting with various world leaders at the G20 Summit in Osaka, Japan.
After having dinner with Mr Moon, President Trump tweeted that he and Mr Moon had “toasted” their new trade deal. He described the deal as a “far better one for us than that which it replaced”.