Park this week said she would be willing to step down early after coming under huge pressure to quit over an influence peddling scandal that has drawn more than a million people onto the streets in protest.
The ruling Saenuri Party's 128 lawmakers unanimously agreed to demand Park resign in late April and called for a presidential election to be held in June, six months earlier than scheduled.
"All the lawmakers of the party unanimously approved this timetable", parliamentary floor leader Chung Jin-Suk was quoted as saying by the Yonhap news agency after a crucial party meeting.
Park said Tuesday she would let parliament decide her fate following accusations that she colluded with Choi Soon-Sil -- a secretive confidante dubbed "Korea's Rasputin" -- to coerce firms to "donate" tens of millions of dollars to foundations which were used for Choi's personal gain.
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Park has been named as a suspect in the investigation, making her the first sitting president to be subject to a criminal probe while in office.
"All South Koreans want Park to leave as soon as possible... They don't want her to stick around so long," its leader Choo Mi-Ae said.
Lawmakers from Park's own party had backed the opposition-led move to impeach her as early as this Friday.
But one of them, former Saenuri Party head Kim Moo-Sung, said they were now willing to give Park four months to leave office.
"If the president agrees to step down on April 30, there is no need to push through with impeachment", Kim said.
"Otherwise, we would have no other option but to take part in the vote for an impeachment motion Friday next week", said Kim, who is leading the anti-Park group within the ruling party.
While she retains the presidency, Park cannot be charged with a criminal offence except insurrection or treason, but she could be charged once she steps down.
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