Democratic Party of Korea Chair Lee Jae-myung, left, shakes hands with People Power Party Chair Han Dong-hoon ahead of their first official talks held at the National Assembly in western Seoul in September. (Yonhap)

Controversies surrounding first lady Kim Keon Hee are likely to top the agenda at the upcoming second meeting between the leaders of the ruling People Power Party and the main opposition Democratic Party, observers said Sunday.

People Power Party Chair Han Dong-hoon and Democratic Party Rep. Lee Jae-myung recently agreed to hold a second round of talks, following up on their first official meeting in early September. The date for the second meeting, however, is yet to be announced.

The agreement comes as the Democratic Party seeks to push for the passage of a bill mandating a special counsel probe into allegations including the ones that the first lady violated the country’s anti-graft law, and the Financial Investment Services and Capital Markets Act, at a National Assembly plenary session next month. The party previously put two similar bills to a vote, but both were scrapped in revotes after Yoon exercised his veto power.

"It is highly likely that the special counsel probe bill will be discussed at the upcoming meeting between Han and Lee," Rhee Jong-hoon, a political commentator said.

"But Han won't agree to the version drafted and floated by the Democratic Party, he is likely to discuss his own solution to the controversies surrounding the first lady," he added.

Han has recently called for appointing an independent inspector general tasked with investigating corruption accusations made against the president's family. The independent inspector general position was established in 2014 under then-President Park Geun-hye but has been left vacant since 2016. Critics suspect that Lee Suk-soo, who was the first independent inspector general, was pressured to step down by the presidential office after he probed Park and her aides.

Park Sung-tae, a journalist-turned-political commentator, said Han's stance on the special counsel investigation bill will determine the outcome of the meeting.

“What’s most important is how Han presents his stance on the special counsel investigation bill,” Park said in a Saturday CBS radio interview.

“The Democratic Party has proposed cutting down on the 13 allegations listed on the special counsel bill, and the focus will be on how Han responds to the offer,” he added.

The agreement between Han and Lee to hold a second round of talks comes amid a snowballing controversy over multiple allegations surrounding the first lady. With Han calling for the first lady to refrain from public activities to restore voters' trust in the conservative bloc, observers detect a growing rift between President Yoon Suk Yeol and the People Power Party leader.

The rival parties, since the first meeting between Han and Lee last month, have cooperated on livelihood issues and passed several related bipartisan bills. However, they have failed to get on the same page over other agenda items, including the special counsel probe bill targeting the first lady.

The latest version of the bill expands the scope of the proposed special counsel investigation to include accusations that the first lady requested Myung Tae-kyun, a self-proclaimed political broker, to conduct public opinion surveys that would favor her husband ahead of the 2022 presidential election.

The first lady's alleged interference in the ruling party's candidate nomination process for the April 10 general election and accusations that she inappropriately meddled in state affairs through her aides in the presidential office were added to the list of allegations.

The first lady's alleged involvement in a stock manipulation scheme and her acceptance of a luxury bag from a Korean American pastor, which were the key allegations in the first two versions of the bill, remained on the list as well.