"I will not forgive anyone responsible for corruption," Park told a meeting of government officials in her first comment on the scandal that was triggered by the suicide of a powerful businessman.
Ordering a thorough and unlimited investigation, Park said it was her administration's responsibility to "root out corruption and complete political reform".
Sung Wan-Jong, the former head of a bankrupt construction company, hanged himself last week on a hillside near his house in Seoul.
Those listed in the memo included Prime Minister Lee Wan-Koo and presidential chief of staff Lee Byung-Kee.
Sung's apparent suicide came as he was about to be questioned by state prosecutors over allegations that he created a slush fund with embezzled company money to bribe politicians and government officials.
In a newspaper interview, Sung said he gave Prime Minister Lee 30 million won (USD 27,000) in cash in 2013 when he was running for a parliamentary seat.
Today, he repeated his denial, but apologised for the fallout from the scandal that has paralysed nearly all parliamentary work over the past week, with angry exchanges between ruling and opposition parties.
The main opposition New Politics Alliance for Democracy has demanded that Lee and other officials named in Sung's note resign.
The affair is a fresh blow to Park, whose popularity ratings were only just beginning to recover from the hit they took after the Sewol ferry disaster a year ago that killed 304 people.
A number of her nominees for senior posts have been forced to withdraw because of allegations of past misconduct.
The prime minister is a largely symbolic post in South Korea where power is concentrated in the executive.
