President Yoon Suk Yeol (right) shakes hands with Han Dong-hoon, interim leader of the ruling People Power Party, during their luncheon meeting at the presidential office in Seoul on Monday in this photo provided by the presidential office. (Yonhap)

President Yoon Suk Yeol and ruling party chief Han Dong-hoon discussed ways to improve the people's livelihoods as they met over lunch on Monday, the presidential office said, their second meeting in less than a week amid efforts to repair their relationship after clashing over allegations involving first lady Kim Keon Hee.

Han of the People Power Party (PPP) attended the luncheon at the presidential office together with PPP floor leader Yun Jae-ok, and the three had lunch for two hours before continuing talks at Yoon's office over tea, Lee Do-woon, senior presidential secretary for public relations, said in a written briefing.

Also in attendance were presidential chief of staff Lee Kwan-sup, senior presidential secretary for political affairs Han Oh-seop and Lee, the senior public relations secretary.

The three agreed to continue negotiations at the National Assembly after the Serious Accidents Punishment Act, which penalizes employers for serious industrial accidents, took effect for companies with fewer than 50 employees on Saturday, so that small business owners "do not experience difficulty," Lee said.

They also had in-depth discussions on housing, transport and other issues related to people's livelihoods.

"The government and the ruling party must double efforts to improve people's livelihoods in a way that can be felt by the people," Yoon was quoted as saying.

Lee made no mention of whether there was any discussion of the recent clash between Han and the presidential office over his handling of allegations the first lady received a luxury handbag as a gift in 2022 and his public support for a PPP emergency leadership committee member seeking to run for a parliamentary seat in Seoul's Mapo Ward.

An official from the presidential office told reporters later that there was "no mention at all" of the allegations against the first lady.

Asked whether Monday's luncheon patched things up, the official said the government and the party are "always in communication."

"We are fully confirming each other's intentions. We have done it before and will continue to do so," the official said.

Han said last week he had rejected the presidential office's request to step down, signaling a potential break with Yoon that threatened to hurt the ruling party with less than three months to go until the April 10 parliamentary elections.

Two days later, Yoon and Han appeared to patch up their differences as they jointly inspected damage from a market fire in the central county of Seocheon and later took the train together back to Seoul.

Yoon and Han are known to have been close for decades since their time as prosecutors.

Yun, the PPP floor leader, confirmed to reporters after lunch there was no discussion of Kim Gyeong-yul, the parliamentary hopeful who has openly demanded an apology from the first lady over the handbag allegations.

Asked whether the first lady issue was brought up, he said, "We talked a lot about people's livelihood issues today." He added negotiations are under way with the main opposition Democratic Party over extending the grace period for small businesses in implementing the Serious Accidents Punishment Act.

Lee, the senior public relations secretary, said Yoon, Han and Yun expressed concern over the recent terror attacks on politicians, apparently referring to the knife attack on DP leader Lee Jae-myung and the brick attack on PPP Rep. Bae Hyun-jin.

Yoon told the party leaders he instructed relevant ministries to swiftly come up with countermeasures, Lee said.