The office of Nepal’s president announced late on Friday that the country would hold elections early next year to replace legislators halfway through their term, a move critics say could further undermine Nepal’s democratic institutions after protests this week led to the government’s collapse.

The announcement, which said elections would be on March 5, came just hours after Sushila Karki, who used to serve as the chief justice of Nepal’s Supreme Court, was sworn in as a caretaker prime minister. The statement from the president, Ramchandra Paudel, said Ms. Karki had picked the date.

Ms. Karki was appointed as an official substitute for K.P. Sharma Oli, the elected prime minister who fled his office during explosive protests this week. Since Monday, more than 50 people have been killed in a wave of violence marked by police abuses and massive property destruction after the government banned social media.

Announcing new elections was the finishing stroke on a series of swift actions that included the dissolution of Parliament and the naming of an interim prime minister within hours.

“Everything about this process is unconstitutional,” said Neel Kantha Uprety, a former chief election commissioner of Nepal who did similar work for the United Nations in Afghanistan. But, he argued, there is no constitutional way forward.