The rapidly emerging political crisis has shocked South Korea.
The country's largest opposition party, the Democratic Party (DP), is demanding that Yoon resign immediately. The party has now formally submitted a proposal to the National Assembly to bring him to trial.
Han Dong-Yoon, leader of Yoon's ruling party, the People's Party (PPP), is demanding that the entire government resign. He also wants the president to be excluded - but the party has agreed not to vote for bringing Yoon to trial, reports news agency Yonhap.
The president "seriously violated the constitution" by introducing martial law, according to the formal request to initiate a trial process obtained by AFP. The president's motive was to avoid investigations into criminal charges against him and his family, the text reads.
Yoon and his wife have been shaken by a series of corruption scandals in recent years.
"Democracy is collapsing"
Defense Minister Kim Yong-Hyun, who is believed to have played a major role in the president's actions, is also threatened with trial. Kim has said he is ready to resign and has apologized.
In Seoul, thousands of demonstrators marched on Wednesday to the presidential office, demanding a trial.
One of the demonstrators, Lim Myeong-Pan, tells AFP that Yoon must resign. The order for martial law was illegal, Lim claims.
He has paved the way for his own trial through this.
First in 40 years
To initiate a trial process, support is required from two-thirds of the parliamentarians and at least six of the nine judges in the country's Constitutional Court.
The opposition parties have a total of 192 of the 300 seats. A vote may possibly take place on Friday.
South Korea's largest trade union umbrella organization, KCTU, is calling for a general strike until the president resigns.
The turmoil was triggered when Yoon Suk-Yeol unexpectedly introduced martial law on Tuesday. The president was forced to back down just six hours later, after parliament voted against the introduction with 190 votes against zero.
It was the first time in 40 years that a South Korean president had declared martial law. Yoon motivated his actions by saying that the opposition was paralyzing the government's work, including by demanding large budget cuts.
