President Park Geun-hye called Monday for a thorough probe into a snowballing bribery scandal after her embattled prime minister offered to quit over his alleged involvement in the scandal that rocked South Korea.

"The prosecution should clearly shed light on everything by conducting a thorough investigation," Park said in a written comment released in Lima, Peru, where she is on a four-day state visit.

She also told officials to ensure that state affairs are not ignored due to the scandal at a time when she is pushing her reform agenda through the National Assembly.

The comment came hours after Prime Minister Lee Wan-koo offered his resignation over a high-profile scandal that involved him and seven other former and current top politicians, mostly close to Park.

"I feel the agony of the prime minister," Park said.

Lee is accused of accepting 30 million won (US$27,000) in cash from a late businessman in 2013, when Lee was running for a parliamentary seat.

Still, Lee has flatly denied the allegation.

The news of Lee's resignation offer overshadowed Park's talks with her Peruvian counterpart, Ollanta Humala, in Lima, the second stop on her visit to South America.

Lee had vowed to stay in his job despite the mounting pressure and Park has said that she will determine Lee's political fate after she returns from the trip early next week.

Lee's resignation offer came more than a month after he declared an "all-out war" on corruption, saying the government will mobilize all its resources to root it out.

But he was later found himself at the center of a bribery scandal sparked by a brief memo left behind by a businessman who committed suicide amid a corruption investigation earlier this month.

Park could accept Lee's resignation offer after she returns from her four-nation swing to South America next week, a presidential official said on condition of anonymity, citing the issue's sensitivity.

In Seoul, Deputy Prime Minister Choi Kyung-hwan will preside over a regular Cabinet meeting on Tuesday, according to the prime minister's office. (Yonhap)