SEOUL—South Korea’s legislature voted to impeach acting President Han Duck-soo on Friday after he declined to make judicial appointments needed to advance the impeachment of his predecessor, extending the political upheaval that began with a short-lived martial law declaration earlier this month.

Han has been the caretaker leader after President Yoon Suk Yeol was impeached by the assembly over his short-lived imposition of martial law earlier this month.

As the president awaits an impeachment trial, the country’s interim leader may, too, be ousted. The currency has plunged as the crisis has deepened.