Park, who is currently recuperating from a stomach ailment following a 12-day South American tour, also promised a sweeping review of "deep-rooted corruption" in Asia's fourth-largest economy.
"I express my regret for causing concerns among South Koreans," Park said in a statement read in a live television broadcast by her chief spokesman Kim Sung-Woo.
"The truths behind the latest scandal should be revealed through a thorough investigation ... we need a new political reform to root out prevalent, deep-rooted corruption in our country," she said.
The president's comments came a day after she accepted the resignation of prime minister Lee Wan-Koo, who had only been in the job a little over two months.
Lee's hand was forced by a scandal triggered by the suicide earlier this month of Sung Wan-Jong, the former head of a bankrupt construction company.
In the dead man's pocket, investigators found a note that listed the names of eight people -- including Lee and former and current presidential chiefs of staff -- alongside numbers that allegedly indicate bribery sums.
The scandal dealt a fresh blow to Park's approval ratings that only recently had started to recover from the aftermath of last year's Sewol ferry disaster.
Bribery scandals involving politicians and rich businessmen have been a fixture of South Korean politics for decades.
Two former presidents served prison terms for taking bribes and dozens of heads of major business groups have been convicted of forming slush funds to lobby politicians.
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