SEOUL (Reuters) - South Korean President Park Geun-hye has retained a lawyer ahead of questioning by prosecutors investigating a favors scandal engulfing her administration, her office said on Tuesday, as she tries to ride out the biggest crisis of her presidency.

The government has been rocked by allegations that a friend used her ties to Park to meddle in state affairs and wield improper influence, triggering calls for Park to be impeached or step down.

She will be the first sitting president to be questioned by prosecutors in a criminal case.

Park's lawyer, Yoo Yeong-ha, a former member of the government's National Human Rights Commission, will discuss arrangements with prosecutors for their questioning, an official at the presidential Blue House said.

The lawyer told reporters that questioning should be kept to a minimum and that he needed time to look into the case.

"If face-to-face questioning is necessary, the number of times should be the minimum," Yoo said, adding that it was improper to investigate a president except on suspicion of treason.

Yoo nevertheless repeated the president's comments that she would make herself available for the investigation.

Park said earlier this month prosecutors should clarify what happened and that everyone involved should be held accountable, including herself, and take responsibility if found guilty.

Park has been criticized over her administration's handling of a ferry disaster in 2014 and the outbreak of the deadly Middle East Respiratory Syndrome the following year, but the current scandal has sparked one of the biggest protests in the country and sent her approval rating to a historical low.

Hundreds of thousands marched in the capital on Saturday demanding that she resign.

Prosecutors are investigating whether Park exerted improper pressure on "chaebol" conglomerate bosses to raise funds for foundations involving her friend, Choi Soon-sil, the Yonhap news agency reported on Sunday.

Yonhap said on Tuesday prosecutors had summoned Lotte Group Chairman Shin Dong-bin, which if true would make him the latest head of a South Korean conglomerate to be questioned by investigators. Lotte Group could not confirm the report and prosecutors were not immediately available for comment.

Other chaebol bosses, including Hyundai Motor Group chairman Chung Mong-koo and Hanjin Group chairman Cho Yang-ho, were questioned last weekend.

Prosecutors are also investigating Choi, who has been detained since Oct. 31.

The leader of the main opposition party proposed talks with Park on Monday but later canceled the offer due to strong party opposition.

Another apology by Park and an offer to work with opposition to form a new cabinet and relinquish some of her powers failed to quell the crisis, prompting opponents to say she did not grasp its severity.

(Reporting by Ju-min Park and Jack Kim; additional reporting by Hyunjoo Jin; Editing by Nick Macfie)