SEOUL (Bloomberg) - South Korean President Park Geun Hye returned from 12 days abroad on Monday facing a government shaken by a widening corruption scandal that may topple the country's second prime minister in a year.

Ms Park needs a day or two of bed rest to recover from fever and stomach cramps that developed from fatigue, her spokesman Min Kyung Wook said on Monday in a statement on the website of her office, citing a medical examination she received upon her return.

Among the decisions awaiting the President after her Latin American tour is whether to accept Prime Minister Lee Wan Koo's offer to step down amid allegations he received 30 million won (S$37,200) from a local businessman. Mr Lee offered his resignation on April 20 after prosecutors began investigating the claims, which the businessman made in a newspaper interview before he was found hanged from a tree in northern Seoul.

The scandal is yet another setback for a South Korean government that has struggled to find stability and energize the economy since a ferry disaster last year killed more than 300, mostly young, passengers. Park also must contend with a special election for four National Assembly seats Wednesday, a potential bellwether for next year's parliamentary poll.

Mr Lee, who has denied taking the money, was Ms Park's third pick for prime minister after Mr Chung Hong Won resigned from the post in the aftermath of the Sewol sinking and two other candidates withdrew their names. He announced a sweeping anti-corruption campaign weeks after his confirmation in February.

"Lee's involvement in the bribery case seriously undermines the administration's credibility," Mr Firat Unlu, Asia analyst at global risk adviser Verisk Maplecroft in Bath, Britain, said in an e-mail. "This diminishes the little political capital Park has to push through necessary structural economic reforms."

Ms Park, 63, has sought to cut regulation, lower taxes and reduce small businesses' dependence on sprawling, family-owned conglomerates such as Samsung Electronics Co. Her goal is to return the economy to a growth rate of 4 per cent by 2017.

Bank of Korea Governor Lee Ju Yeol on April 9 lowered the central bank's forecast for gross domestic product growth this year to 3.1 per cent from an estimate of 3.4 per cent in January. The economy grew 2.4 per cent in the first quarter, the Bank of Korea said Thursday, rebounding from its slowest expansion since 2009 in the previous three months.

The allegations against the Prime Minister emerged just as Ms Park was preparing to attend a memorial for the anniversary of the Sewol disaster and depart for her trip to Colombia, Peru, Chile and Brazil. The source was a note found April 9 with the body of Mr Sung Wan Jong, the head of Keangnam Enterprises.

The note included the names of eight Park political allies, including Mr Lee, followed by six numbers believed to be monetary amounts. Hours before his death, Mr Sung had told the Kyunghyang Shinmun newspaper that he had in 2013 given money to Mr Lee, who was then running for a National Assembly seat.

Mr Sung also told the paper he gave 200 million won to a senior aide to Ms Park's 2012 presidential campaign. The note listed a name identical to Ms Park's chief of staff Lee Byung Kee someone he did not speak in detail about in the Kyunghyang interview.

A special team of prosecutors under Justice Minister Hwang Kyo Ahn is investigating the case.

"The memo about eight people is the starting point, but the investigation won't be limited to particular people singled out by a particular person," Mr Hwang told an April 20 parliamentary hearing. "This is the time to conduct a comprehensive review of illegal political funds coming and going in the political circles."

Ms Park has said she supports a thorough investigation. The President doesn't want the scandal to "divide the nation" and slow her economic agenda, her spokesman Min said in a televised briefing last week.

The President's approval rating rose 1 percentage point last week to 35 per cent, Gallup Korea said on Friday. Her support fell to a record low of 29 per cent in January after allegations that a former aide attempted to influence the decisions of her office. Prosecutors concluded those claims were unfounded.

The new graft case undercuts efforts by Ms Park's Saenuri Party to pick up four National Assembly seats formerly held by a minority party disbanded for supporting North Korea. A strong showing by the New Politics Alliance for Democracy could give the opposition party a boost ahead of next year's vote.

"Lee's resignation offer was the best option possible to minimize repercussions from the scandal," Mr Hwang Tae Soon, a political analyst at the Wisdom Centre in Seoul, said by phone. "It may help unite conservative voters in the by-elections."