South Korea's ruling party on Thursday urged scandal-hit President Park Geun-Hye to step down in April next year, giving her a week to accept their ultimatum or risk impeachment.

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.

The party considered the timetable the most appropriate to ensure a peaceful transfer of power, maintain stability and give political parties time to prepare for the presidential election, Chung said.

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.

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.

And although Park's announcement reduced the momentum of calls for her impeachment, the main opposition Democratic Party insisted that Park should be stripped of office by the end of January.

"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.

- Four month deadline -

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.

The party would give Park until Thursday next week to accept their demand.

"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.

Massive weekly protests have been intensifying over the past month, with up to 1.5 million people braving freezing temperatures in Seoul on Saturday to demand Park's resignation, according to organisers.

Activists called for a sixth weekly protest on Saturday in central Seoul, despite Park saying she would be willing to cede power.

Park on Wednesday approved a lawyer recommended by the opposition-controlled parliament as an independent prosecutor to carry out a new probe into the scandal.

The special prosecutor will interview Park and be given 120 days to follow up on the findings of state investigators.

She has backtracked on earlier promises to make herself available for questioning in a judicial probe.