First lady Kim Keon Hee arrives at Hickam Air Force Base in Honolulu, Hawaii, July 9. Yonhap

Rival parties continued to clash on Friday over a bill calling for a special counsel investigation into allegations involving first lady Kim Keon Hee, including claims of her alleged involvement in the candidate nomination process for the parliamentary elections.

The main opposition Democratic Party of Korea (DPK) and minor opposition Rebuilding Korea Party again proposed a bill, Thursday, calling for a special counsel probe into various allegations surrounding Kim, accusing her of meddling in the ruling People Power Party (PPP)'s candidate nomination process for the April 10 general elections.

The DPK accused Kim of exerting influence to persuade former lawmaker Kim Young-sun of the PPP to change her district for the elections.

"Reasons to launch a special investigation into the first lady continue to accumulate," Rep. Park Chan-dae, floor leader of the DPK, said during a party Supreme Council meeting, Friday. "If the reports of her election meddling are true, it represents a manipulation of state affairs for which the administration should be held accountable. It is only fair to investigate allegations against the president's wife and impose penalties if she is found guilty. I hope the president and the PPP will support our bill for a special counsel to investigate these claims."

The presidential office denied any involvement by Kim, saying that candidate selection was decided by the PPP's nomination committee.

"Kim Young-sun was cut off following the committee's decision and, as a result, was not nominated for any electoral district. So what kind of interference is this?" a senior presidential official said.

The parties initially proposed similar bills that included allegations of Kim's involvement in stock manipulation, accepting a luxury bag from a pastor, and claims that the government altered the route of an expressway project to benefit her family financially.

However, President Yoon Suk Yeol vetoed the bills, sending them back to parliament for reconsideration. The National Assembly subsequently rejected the bills in a revote, leading to their automatic dismissal.

The PPP accused the DPK of attempting to promote conspiracy theories.

"The DPK is once again raising irrational conspiracy theories against the first lady based on unconfirmed reports. We know its purpose is to stir political debate by bringing up special counsel probe bills and parliamentary hearings," Rep. Park Jun-tae, spokesperson of the PPP, said.

Rep. Na Kyung-won of the PPP claimed that the DPK's call for a special counsel investigation into Kim is part of a broader strategy aimed at building a case for the president's impeachment.

"The DPK's accusations against the first lady are just madness. It has been engaged in negative political framing campaigns aimed at tarnishing the image of female politicians. Framing Kim as a bar hostess using the nickname 'Julie' is despicable, "she wrote on her Facebook, Friday.