SEOUL (Reuters) - South Korean prosecutors will question President Park Geun-hye over a political corruption scandal engulfing her presidency, an official said on Sunday, the first time a sitting president will be questioned by prosecutors over a criminal case.

South Korean President Park Geun-Hye speaks during an address to the nation, at the presidential Blue House in Seoul on November 4, 2016. REUTERS/Ed Jones/Pool

Hundreds of thousands marched in the capital Seoul on Saturday demanding Park resign. Many protesters said Park, whose public support has dropped to the lowest point ever for a democratically elected South Korean leader at 5 percent, was unfit to rule.

Prosecutors are investigating whether Park exerted improper pressure on “chaebol” conglomerate bosses to raise funds for two foundations at the center of an influence-peddling scandal involving a friend of hers, Yonhap reported on Sunday, citing prosecution sources.

They are also probing Park’s friend, Choi Soon-sil, who is alleged to have used her ties to the president to meddle in state affairs and wield influence in the cultural and sports communities, a prosecutor has previously said.

Prosecutors have already questioned the de facto head of Samsung Group SAGR.UL Jay Y. Lee and the chairmen of Hyundai Motor Group 005380.KS and Hanjin Group HANJ.UL over the scandal, media reports said on Sunday.

“It’s correct we’re planning to question the president but the date is undecided,” an official at the prosecutors’ office told Reuters.

Yonhap news agency quoted a prosecution official as saying Park’s questioning should be done no later than Wednesday.

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“Questioning people face-to-face is our principle,” the official said. Park will appear before prosecutors as a witness, Yonhap reported.

Park’s office said it would be Tuesday at the earliest before it will have a position on the prosecutors’ plan and was considering retaining a lawyer for the president.

While some previous South Korean presidents have been mired in scandals or allegations of wrongdoing involving family members during their terms, none were directly questioned by prosecutors while they were in office.

The prosecution office official confirmed the chairman of Hyundai Motor, Chung Mong-koo, was questioned on Saturday but declined to confirm whether the other chaebol bosses had met prosecutors.

A Korean Air Lines 003490.KS spokesman confirmed that Cho Yang-ho, who is chairman of Hanjin and South Korea's largest airline, had appeared for questioning but did not elaborate further.

A Hyundai Motor spokesman declined to comment and Samsung Group could not immediately confirm the reports of prosecutors questioning their respective officials.

Park faces intense pressure from the public and parliament to step down over the scandal, but the main opposition parties have not raised the possibility of initiating impeachment proceedings.

The presidential office said earlier on Sunday that Park was “earnestly considering ways to normalize state affairs” and that she had “heard the voices of the people at the rally”.

Park has said she had discussed with conglomerate heads in July last year her desire for them to contribute more for culture without elaborating.

South Korean prosecutors raided Samsung Electronics last week as part of the probe over the scandal and whether the company separately gave millions of euros to a company controlled by Choi and her daughter.

(This story was refiled with full name of Hanjin chairman in paragraph 12)