SEOUL -- South Korean prosecutors plan to investigate President Park Geun-hye early next week over Park's biggest political scandal involving her longtime confidante Choi Soon-sil suspected of intervening in state affairs behind the scenes and peddling undue influence for personal gains.

According to local media reports, a special investigative unit under the Seoul Central District Prosecutors' Office in charge of investigation into the case has delivered to the presidential Blue House its request to investigate the scandal-plagued president on Tuesday or Wednesday.

If realized, Park would become the first South Korean president to be investigated by prosecutors as incumbent leader. Under the country's constitution, a president is free from criminal indictment, but some of law experts claim a criminal investigation is possible if the indictment is suspended until the end of presidency.

Park, who took office in February 2013, has about 15 months left in her single, five-year term.

Face-to-face investigation is preferable in principle, the prosecution said, but details haven't been decided upon where and how to prove the embattled president. It added that President Park would be a reference witness during an investigation.

The scandal-hit president made public apologies twice since the scandal came into focus last month, but public anger hasn't been appeased.

The largest mass rally in three decades was held on Saturday night to demand Park's immediate resignation. Organizers said about 1 million protesters took to the streets in Seoul alone, the biggest since the identical number of people protested against the military dictatorship in June, 1987.

Police estimated that around 260,000 people turned out in Seoul. Police estimates are usually far lower than the figures released by organizers as people coming back home after early participation are not included in calculations.

Thousands of people are expected to continue rallies in major cities nationwide, including Seoul and the southern port city of Busan where some 30,000 residents marched to call for the president's resignation the previous night.

Meanwhile, prosecutors summoned chiefs of key conglomerates, who are alleged to have closed-door meetings with President Park last year, over the weekend.

The first South Korean female leader held an open meeting with 17 chiefs of conglomerates on July 24 last year, and had closed-door meetings, separately one by one, with seven of them until the following day.

Samsung Electronics Vice Chairman Lee Jae-yong and chiefs of LG Group and CJ Group were summoned on Sunday afternoon. Hyundai Motor Group Chairman Chung Mong-koo and two heads of Hanwha Group and SK Group were grilled on Saturday over the behind-the-scenes meetings with President Park.

Choi Soon-sil, 60, is alleged to have pressured big companies into donating 77.4 billion won (66.3 million U.S. dollars) to two nonprofit foundations she actually controls. Choi, whose friendship with Park dates back to the mid-1970s, has been arrested for abuse of power and attempted fraud.

Samsung made the biggest donation of 20.4 billion won to the Mir and K-Sports foundations, with 12.8 billion won, 11.1 billion won, 7.8 billion won and 2.5 billion won each donated by Hyundai, SK, LG and Hanwha. The donation scale is roughly in line with rankings in terms of wealth.

The Samsung vice chairman has also been questioned about why Samsung transferred 28 billion euros (about 30 billion U.S. dollars) last year to a company in Germany co-owned by Choi and her 20-year-old daughter.

Samsung in charge of the Korea Equestrian Federation claims that it was sent to support six horse riders, but the money was spent solely on Choi's daughter who was previously a member of the national equestrian team.