Six lawmakers from the Democratic Party called for Park's resignation, marking the first time that members of the main opposition party openly demanded she step down.
The small, progressive Justice Party has been the only political entity at the National Assembly to officially demand the resignation, although Rep. Ahn Cheol-soo, a potential candidate for next year's presidential race from the minor People's Party, also called for her to give up her presidency.
Other key figures from the opposition bloc often cited as influential contenders in the upcoming election, including Seoul Mayor Park Won-soon, have started to demand Park's resignation amid mounting public anger toward Choi Soon-sil. Choi is seen as a behind-the-scene figure who used her long-standing ties to Park to exert power over state affairs.
"Park's ability to lead state affairs is now destroyed," the six lawmakers said in a statement.
"Park's prolonged rule will bring extreme confusion, leaving the country in a deadlock. The people will become victims," they added. "There will be disaster if Park does not step down and continues to cling to her remaining term in office."
Park's single five-year term ends in February 2018.
The lawmakers highlighted that South Korea's Constitution will allow the country to hold a presidential election within 60 days of the resignation, which will be helpful in resolving the crisis.
"Park should give up her power and authority, before the people fully turn their backs on her," Ahn also said. "This is not an issue of being liberal or conservative. It is about right and wrong."
The Democratic and People's Party, however, are still refraining from officially asking for Park's resignation, while calling for a thorough investigation into the scandal.
In an effort to seek a breakthrough, the presidential office has been announcing personnel changes since Wednesday, nominating figures who served during the liberal administrations of Kim Dae-jung and Roh Moo-hyun to key posts in the Cabinet and presidential secretariat.
The opposition bloc, however, vowed to boycott the shakeup, which did not take the parliament's opinion into consideration.
"If (the presidential office) attempts to dodge crises or try to drag out time with short term measures, there will be more crises," said Rep. Woo Sang-ho, the floor leader of the Democratic Party. "Park should confess to the wrongdoings and apologize. She should volunteer to be questioned."
Woo added the controversy surrounding the personnel change does not center on whether the people are "good or bad," but the focus is on how Park will change the way she runs state affairs.
Rep. Lee Jung-hyun of Saenuri said he thinks the president is considering a move to hold talks with leaders from the opposition parties on key issues, adding he is also open to discussions at anytime.
Lee said it would have been better if Park consulted with the parliament before announcing the personnel reshuffle.
Political pundits, however, have said that Saenuri is facing a crisis over the discord among different factions. While the non-Park faction demands the resignation of the party leadership, those that are loyal to the president are digging in their heels.
Park supporters maintain the crisis must be settled before any resignation of the party leadership.
Justice Minister Kim Hyun-woong, meanwhile, said he will consider the option of posing questions directly to Park if it is deemed necessary to get to the bottom of the matter.
"Legal experts made clear that the president cannot be summoned for questioning," Kim said, but added there are no limits if Park volunteers to answer questions. (Yonhap)