Speaking after confidante Choi Soon-sil and two aides were charged, Chief Prosecutor Lee Young-ryeol said Ms Park was "involved as a conspirator".
Ms Park's lawyer said that prosecutors had "built a house of fantasy".
The president has immunity from prosecution but has faced huge protests and opponents have urged her to quit.
Chief Prosecutor Lee said the president would be questioned soon.
However, although she had previously pledged to co-operate in the investigation, her lawyer, Yoo Young-ha, said on Sunday that Ms Park would not meet prosecutors and would only deal with an independent team that will soon take over the inquiry.
Ms Park's spokesman, Jung Youn-kuk, said that the prosecutors' allegations were "unfair political attacks".
He said their case was "a house of cards built on imagination and speculation that completely ignores objective evidence".
Ms Park, whose approval rating has dropped to 5%, has apologised twice on national television but has so far resisted calls to resign.
South Koreans have reacted angrily to the revelations. The country has witnessed the largest protests since the pro-democracy demonstrations of the 1980s.
Organisers said as many as 500,000 people attended a candlelit rally in the capital this weekend, which brought streets to a standstill for the fourth consecutive Saturday. Police put the figure far lower.
The opposition may attempt to impeach Ms Park if she stays in office in order to protect her immunity. She can be charged once she is no longer president.
Ms Choi is accused of trying to extort huge sums of money from South Korean companies, and is suspected of using her friendship with Ms Park to solicit business donations for a non-profit fund she controlled.
Also indicted was Ahn Jong-beom, Ms Park's former senior secretary for policy co-ordination. Mr Ahn was charged with abuse of authority, coercion and attempted coercion.
The second aide to be charged was Jung Ho-sung, accused of passing classified presidential documents to Ms Choi, including information on ministerial candidates.
South Korean President Park Geun-hye had a "considerable" role in a corruption scandal involving a close confidante, prosecutors have said.