SEOUL (Reuters) - South Korean opposition parties vowed on Wednesday to push ahead to try to impeach President Park Geun-hye amid a growing influence-peddling scandal, rejecting her offer to resign, and called on members of her Saenuri Party to join them.

In a dramatic move that shifted the burden of resolving the crisis engulfing her presidency, Park asked parliament on Tuesday to decide how and when she should quit, which opposition lawmakers dismissed as a ploy to buy time and avoid impeachment.

The leaders of the three opposition parties, which together hold 165 of the single-chamber parliament’s 300 seats and can initiate an impeachment motion, said they would not negotiate with Park’s party on her proposal to step down.

“The only way left to go is impeachment under the constitution,” the head of the Democratic Party, Choo Mi-ae, said at a meeting with the leaders of two other opposition parties.

The leader of the opposition People’s Party, Park Jie-won, said a motion would be put to a vote on Friday, or on Friday week if necessary.

“Impeachment is the only way,” he said.

Park, who has immunity from prosecution in the case as long as she remains in office, is alleged by prosecutors to have colluded with a friend, Choi Soon-sil, to enable her to wield improper influence in government affairs and in fundraising by two foundations set up to back Park’s initiatives.

She has denied wrongdoing but acknowledged carelessness in her ties with Choi.

Park appointed a special prosecutor who will take over the probe by state prosecutors that was widening to include former government officials and conglomerate heads and also tried to question the president herself.

Park has said she would cooperate with the work of the special prosecutor, whom she appointed from two candidates nominated by the opposition under a bill passed two weeks ago.

SAENURI IN DISARRAY

Park Young-soo, who is not related to the president, will lead a team of more than 100 investigators.

“Our focus will be strictly on finding the truth and will not limit the scope of our investigation or have consideration for whether the people being questioned are high ranking or not,” Park told reporters.

Slideshow ( 11 images )

The opposition needs a minimum of 28 votes from Saenuri to pass the impeachment bill, which will immediately suspend Park’s powers while the Constitutional Court takes up to six months to decide the validity of the motion.

The court could take as little as two months, most legal experts said. If Park is unseated, a new election must be held in 60 days to pick a successor for a full five-year term.

The prime minister, normally a figurehead post, would serve as acting head of state in the interim.

Slideshow ( 11 images )

Saenuri has been in disarray over the crisis.

Party floor leader Chung Jin-suk said it would be best to set a deadline of April 30 for Park to step down, but a breakaway faction of more than 40 members demanded she leave sooner.

Hwang Young-cheul, a member of the breakaway group, said on Tuesday it was willing to negotiate for an exit plan for Park but if all sides failed to reach an agreement by Friday week, it would join the opposition’s impeachment motion.

The crisis has started to weigh on consumer confidence and has dealt a blow to the reputation of the “chaebol” conglomerates, accused of kowtowing to Park.

Finance Minister Yoo Il-ho said on Wednesday the economy faced greater downside risks due to the crisis and a recovery was showing signs of slowing because of uncertainties in South Korea and abroad.