Geun-hye's stunning announcement on Tuesday comes after massive protests that have called for her ouster amid a mounting scandal.
Opposition parties have been closing in on an impeachment motion against her and even her allies in the conservative ruling party have called for her to "honourably" step down rather than face impeachment.
Park had previously been rejecting calls to leave office and dismissed prosecutors' claim that she colluded with a confidante who allegedly manipulated power from the shadows and extorted companies to amass an illicit fortune.
I will leave the matters about my fate, including the shortening of my presidential term, to be decided by the National Assembly," Park said in a live address to the nation, referring to parliament.
"If the ruling and opposition parties discuss and come up with a plan to reduce the confusion in state affairs and ensure a safe transfer of governments, I will resign from the presidential position under that schedule and by processes stated in law."
Opposition parties had been closing in on an impeachment motion against Park, and even her allies in the conservative ruling party have called for her to "honourably" step down rather than face impeachment.
An impeachment motion vote had been planned for Friday. The country's two largest opposition parties were also planning on Tuesday to nominate a special prosecutor to independently investigate the scandal.
At the heart of the scandal is Choi Soon-sil, Park's longtime friend and the daughter of a late cult leader who allegedly meddled in state affairs and pressured companies to donate millions of dollars to foundations controlled by her at the request of Park.
Prosecutors have so far indicted Choi, two ex-presidential officials and a music video director known as a Choi associate for extortion, leakage of confidential documents and other charges.
Park, who has immunity from prosecution while in office, has refused to meet with prosecutors. Her lawyer, Yoo Yeong-ha, has described prosecutors' accusations against Park as groundless.
The main opposition Democratic Party later rejected Park's offer, calling it a ploy to escape being impeached, Yonhap news agency said.
Park Kwang-on, a Democratic Party MP, said it looked like she was trying to delay proceedings.
"She is handing the ball to parliament, when she could simply step down," he said.
"She is asking the parliament to pick a date for her to resign, which she knows would lead to a discussion on when to hold the presidential election and delay everything."
