SEOUL — South Korea’s main opposition parties threatened Monday to impeach the country’s acting leader after he refused to extend a special investigation into the huge corruption scandal that toppled conservative President Park Geun-hye.

If successful, the impeachment of Prime Minister Hwang Kyo-ahn would rile an already tumultuous political landscape, putting another interim leader in power while the Constitutional Court decides the fate of both Hwang and Park, who is now on trial.

Hwang refused a request by the investigation team to extend its probe past Tuesday’s deadline. A spokesman for Hwang said the team led by independent counsel Park Young-soo has already indicted key figures implicated in the scandal and that state prosecutors can look into any other areas.

Prosecutors say Park allowed her confidante to meddle in state affairs and that they colluded to extort money from companies.

The three main liberal opposition parties spearheaded Park’s December impeachment and vowed immediately to push for Hwang’s.

His decision shows he’s trying ‘‘to become Park’s shield to protect her and her associates,’’ said Choo Mi-ae, leader of the opposition Democratic Party.

Impeaching a prime minister requires support from half of the 299-member Parliament.

Associated Press