Rebuilding Korea Party leader Cho Kuk, known for his vocal criticism of President Yoon Suk Yeol, demanded Monday that Yoon accept a special counsel probe into allegations involving first lady Kim Keon Hee.

The demand was among 10 requests that Cho said Yoon should accept in accordance with the public sentiment revealed in this month's parliamentary elections in which Yoon's People Power Party suffered a resounding defeat.

"These are the minimum 10 things for President Yoon Suk Yeol to carry out in line with the public sentiment revealed in the April general elections," Cho said in a Facebook post.

Many of the demands are that Yoon accept a series of bills that he has previously vetoed, including one calling for a special prosecutor investigation into allegations that the first lady was involved in stock price manipulation between 2009-2012.

Cho also demanded Yoon accept a special probe into allegations that the presidential office inappropriately interfered with a military probe into last year's death of a young Marine who was swept away by heavy currents while on a search operation for downpour victims.

To the main opposition leader, Lee Jae-myung, Cho proposed Lee hold a meeting with all opposition party leaders to gather opinions before he meets the president this week.

"I'd like to take this opportunity to respectfully ask Chairman Lee to form and lead a panopposition joint conference before meeting President Yoon," Cho said during an event in Jeonju, North Jeolla Province.

"Collecting opinions from opposition leaders will carry much more weight," Cho said, adding that he will be waiting for Lee's response.

Yoon and Lee are set to have their first-ever meeting sometime this week after Yoon called the other last week to meet at the presidential office.

Yoon has been under increasing pressure to seek cooperation with the opposition bloc after the ruling PPP's crushing defeat in the elections.

Cho also pointed out that Lee will be representing all of the 192 seats won by the wider opposition, not only the 175 seats his Democratic Party clinched in the elections.

"I dare say this, Chairman Lee should be the leader of the 192 seats," Cho added.

Cho is a former justice minister who fell into disgrace following an investigation into academic fraud involving his children when President Yoon was prosecutor-general. He launched the Rebuilding Korea Party just about a month before the April 10 parliamentary elections.

After campaigning with calls for bringing an early end to the Yoon administration, Cho's party won 12 proportional representation seats to become the third-largest party in the incoming National Assembly. (Yonhap)