S. Korea prosecutors want to question president over scandal

If Park agrees, it will be the first time a sitting president has been questioned by prosecutors.

The scandal is the most serious challenge for Ms Park, whose public apologies have done little to calm public anger.

"It is correct, we are planning to question the president but the date is undecided", an unnamed official at the prosecutors' office told Reuters news agency on Sunday.

President Park Geun-hye leaves the podium at the Blue House in Seoul after reading an apology on November 4.

Her presidency has been rocked by the suspicion that she let a longtime confidante manipulate power from behind the scenes.

Also subject to key investigations will be alleged favors granted to Choi's 20-year-old daughter when entering a prestigious university and 2.8 million euros (about 3 million USA dollars) transferred by Samsung to a company co-owned by Choi and her daughter.

Lee Ryeo-hwa, a Seoul resident who brought her three children to the rally, the youngest of them hanging on her front in a baby carrier, said Park had to go because she "created this mess with her undemocratic leadership style and refusal to communicate".

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If Park is investigated by prosecutors, she would become the first South Korean president subject to criminal investigation as incumbent leader. Statements from the presidential office have merely indicated that Ms Park will exercise her lawful authority as enshrined in the constitution, such as her control over the armed forces, and would try to get things back on track.

Having overseen the introduction of tough anti-corruption legislation since she began a five-year term in 2013, Park has been linked to a scam in which large conglomerates allegedly bought favors via presidential aides and a private confidante, Choi Soon-sil.

The family-friendly protest was peaceful but sometimes reached deafening volumes as performers and activists whipped the crowds into a raucous frenzy from a giant stage.

Lee Jae-myung, the mayor of Seongnam, Gyeonggi, who recently said the time has come to use impeachment to get Park to step down, wrote on his Facebook account Sunday that he would consider officially requesting the prosecution to dig in on Park's whereabouts on the day of the Sewol ferry tragedy on April 16, 2014.

"The face-to-face questioning of President Park should be conducted by this Tuesday or Wednesday at the latest".

"Her resignation would effectively mean that she's open to be investigated under arrest", said Ms Park Tae-woo, a commentator and professor at Korea University's Institute of Sustainable Development.

As the South's largest business conglomerate by far, Samsung also faces allegations that it separately offered millions of euros to Choi to bankroll her daughter's equestrian training in Germany.