President Yoon Suk Yeol (right) and People Power Party Chair Han Dong-hoon stroll along as they attend a dinner hosted by the presidential office on July 24. (Presidential Office)

President Yoon Suk Yeol told the ruling People Power Party Chair Han Dong-hoon to embrace his political allies as they sat down for closed-door talks for about 1 1/2 hours Tuesday morning, the president's office said Wednesday.

It was among the agenda items discussed at the highly anticipated meeting of Yoon and Han that took place in the presidential office from 11 a.m. to 12:30 p.m. -- 30 minutes longer than initially planned. Yoon's chief of staff Chung Jin-suk was also in attendance throughout the meeting, according to an official of the presidential office on condition of anonymity.

The presidential office, however, added there was no discussion of its plan to establish the first lady's office.

A reorganization of the presidential office to set up the first lady's office was unveiled Tuesday, counter to Yoon's 2022 campaign promise not to have a separate administrative office supporting his wife. The presidential office added that no decision over who would lead the new office has been made.

Also, a special counsel bill potentially targeting Yoon -- over which Han has hinted at compromising with opposition parties -- was among the items on the agenda during the meeting.

The meeting, the first exclusive face-to-face between the leaders of the government and the ruling party, was proposed by the People Power Party.

The meeting came amid rumors over a lingering ruling bloc rift between the conservative president and newly elected leader of the conservative party, despite the many years the two worked together as prosecutors. Rumors have circulated over the two locking horns with each other after Han entered politics in December as the interim party leader.

Rumors of the two bickering intensified after it was revealed during the campaigning period for the party convention last month that Han did not reply to text messages from first lady Kim Keon Hee early this year over whether she should apologize to the public for her alleged violation of the antigraft rule by receiving a luxury Dior bag as a gift. Yoon's office had also suggested Han resign from the interim People Power Party chair post in January, which he refused to do.

Meanwhile, Yoon was also quoted as saying by Rep. Park Jeong-ha of the People Power Party, Han's chief secretary, that the party's affairs are in the hands of the party chair and asked Han to take various opinions into account.

Park added it is "desirable" for Han to hold frequent meetings with Yoon, calling Tuesday's meeting "a good sign in itself."

Rep. Shin Dong-wook, spokesperson of the People Power Party, also said in a radio interview that the closed-door meeting was a "signal of reconciliation."

This came amid an internal feud between lawmakers of the People Power Party over the fate of Rep. Jeong Jeom-sig, who is currently the policy chief of the party. Han, who won the top spot at the party convention on July 23, has the authority to replace Jeong, who is currently one of the nine members of the party's Supreme Council. According to Yoon's office, no specific name for such a figure was brought up during the meeting between Yoon and Han.