The new ruling People Power Party leadership kicked off its first day by highlighting unity amid concerns over lingering tensions between President Yoon Suk Yeol and newly elected party Chair Han Dong-hoon.

The two met for dinner at the presidential office in Yongsan-gu in Seoul at the invitation of the president, Yoon's office said, noting that the meeting was intended to nurture "a grand harmony." Han was invited along with some other contenders at the party's national convention and the elected members of the ruling party's supreme council.

An official, speaking on condition of anonymity, said that Yoon is open to a one-on-one meeting with Han, but did not elaborate on the details of the arrangement. The exclusive meeting could take place as soon as Wednesday or later on, she added.

This comes as the main opposition Democratic Party of Korea on Wednesday urged Han to press the party's demands concerning vetoed bills related to the launch of special counsel investigations into allegations involving Yoon himself as well as his family.

During a party meeting at the National Assembly, Rep. Park Chan-dae, acting chair of the Democratic Party, urged the ruling party to join the opposition in a unanimous bipartisan vote in favor of the special counsel bill to investigate the case of a young Marine conscript's death and override the president's veto.

The bill, which Yoon previously vetoed, is aimed at launching a special counsel to look into alleged state interference -- potentially targeting Yoon himself -- that the main opposition claims had allowed a Marine Corps. division commander to evade police interrogation. The bill is on the verge of a revote, which requiring at least 200 votes in the 300-member National Assembly to override the veto.

Meanwhile, a special counsel bill demanding a special counsel probe into Han, which would look into his alleged professional negligence as a prosecutor, was tabled in the National Assembly's legislation and judiciary committee on Wednesday.

All eyes are on whether Han will accept the demands of Yoon's political opponents, who control the majority of the National Assembly but still fall short of the power to override a presidential veto.

On Wednesday, Han reiterated his stance of considering having the ruling party propose its own version of the special counsel bill, specifying a fairer way of recommending or determining a special counsel into allegations involving Yoon and his family than the vetoed bill that rules out the ruling party's participation in the nomination process.

Not all elected leaders of the party appear to be on the same page.

Kim Jae-won, a newly elected supreme council member who served three terms as a lawmaker, said Wednesday in a radio interview that a floor leader's opinion "takes precedence" over that of the party chair if their opinions differ, regarding the party's approach to a special counsel bill. Rep. Kim Min-jeon echoed Kim Jae-won in a separate radio interview, as he said Han does not have the power to determine the party line.

Han, 51, was recently interim chief and returned to the ruling party chair post in a resounding victory Tuesday. He opened the first day as the party's chair by visiting Seoul National Cemetery together with the party's key decision-makers.

Accompanying Han were newly elected supreme council leaders -- former lawmaker Kim Jae-won and Reps. Jang Dong-hyeok, Kim Min-jeon, Yohan Ihn and Jin Jong-oh -- as well as key decision-makers such as Floor Leader Rep. Choo Kyung-ho, policy chief Rep. Jeong Jeom-sig and Secretary General Rep. Sung Il-jong.

"I will pay closer attention to people, explain more to people and persuade more people to win hearts of the people and go hand in hand with them toward the future," Han wrote in the guestbook.

Han later on Wednesday greeted Hong Chul-ho, senior presidential secretary for political affairs, at the National Assembly before joining a dinner hosted by Yoon.

Han, a prosecutor-turned-politician, was elected Tuesday as the chair of the People Power Party with 62.8 percent of the vote at the national convention in Goyang, Gyeonggi Province.

Han, who served as the interim chair of the party from December until April, overcame former Land Minister Won Hee-ryong and Reps. Na Kyung-won and Yoon Sang-hyun. Before the 22nd National Assembly, Won served three terms as a lawmaker. Na and Yoon are each serving a fifth term in the parliament.