Rep. Lee Jae-myung, left, leader of the main opposition Democratic Party of Korea (DPK), shakes hands with Kweon Seong-dong, acting leader and floor leader of the ruling People Power Party (PPP), before their meeting at the National Assembly in Seoul, Wednesday. Yonhap

The leaders of the ruling People Power Party (PPP) and the main opposition Democratic Party of Korea (DPK) held talks Wednesday for the first time since the National Assembly impeached President Yoon Suk Yeol last Saturday over his attempt to impose martial law.

Although the two sides agreed to resolve the political crisis and reduce their political offensives, the meeting ended without any resolution to their differences on thorny issues. Contentious topics included withdrawing impeachment bills against public officials and senior prosecutors, and forming a joint consultative body between the government and the Assembly to manage state affairs.

Rep. Kweon Seong-dong, acting leader and floor leader of the PPP, asked the main opposition to withdraw several impeachment bills it passed to ease the political turmoil.

"There are 14 impeachment bills pending before the Constitutional Court. Now that trial proceedings over Yoon's impeachment have been added, I doubt whether the Constitutional Court will be able to handle them all," Kweon said. "I hope the DPK withdraws politically motivated impeachment bills in order to ease the burden of the court."

The PPP's acting chief welcomed DPK leader Rep. Lee Jae-myung's call for the swift replacement of former Defense Minister Kim Yong-hyun, who resigned in the aftermath of the martial law declaration and has been arrested for his role in Yoon's martial law order.

On the other hand, the DPK leader sought cooperation in implementing a supplementary budget and requested the ruling party to join the consultative body to stabilize state affairs.

"I think it's urgent to implement the supplementary budget to stabilize the people's livelihoods," Lee said. "Kweon seems to have a slightly pessimistic view on the Assembly-government consultative body that I proposed earlier, but we are willing to make concessions to some extent. I think both parties can have open channels and negotiate on this matter further."

Earlier, Kweon refused Lee's request by saying "Lee should not act as though he has already become president."

A special committee holds a meeting to discuss the confirmation process for three Constitutional Court justice nominees at the National Assembly in Seoul, Wednesday. Yonhap

Filling the Constitutional Court's three vacant seats wasn't on the meeting's agenda, according to officials familiar with the matter.

The two parties have been at odds over the appointment of the new constitutional judges.

On Tuesday, Kweon claimed that acting President Han Duck-soo lacks the authority to appoint a justice to the Constitutional Court until the impeachment motion is upheld, but DPK floor leader Rep. Park Chan-dae said that it is within Han's authority to approve the appointment of the three judges nominated by the National Assembly.

The Constitutional Court requires at least six justices to uphold Yoon's impeachment. The court consists of nine judges — three appointed by the president, three by the chief justice and three by the National Assembly.

However, the three seats to be recommended by the National Assembly are empty due to disputes between the ruling and opposition parties.

The PPP put forward Cho Han-chang, a former judge at the Seoul High Court, while the DPK nominated two judges from the Seoul Western District Court: Jung Gye-seon and Ma Eun-hyeok.

This leaves the court to decide whether it will proceed with Yoon's impeachment case with only six justices or wait until the vacant seats are filed.

Deliberation of the impeachment case is possible with just six, the Constitutional Court reaffirmed recently, as the legal mandate for seven justices has been temporarily suspended since November.

The National Assembly will hold confirmation hearings on the three nominees on Dec. 23 and 24.