Opposition leader Chandrababu Naidu, center, began a hunger strike in New Delhi on Monday to protest plans to divide Andhra Pradesh state Associated Press

NEW DELHI—Indian police imposed an indefinite curfew and issued shoot-on-sight orders to enforce it in parts of a southern state torn by violent protests against a central government plan to cut it in two.

Since a decision last week by India's cabinet to carve a new state, Telangana, from the state of Andhra Pradesh, demonstrators have repeatedly clashed with police, throwing rocks and setting fire to vehicles and buildings.

Adding to the turmoil, power-utility workers in the region have gone on strike, leading to blackouts in some towns and villages and disrupting traffic on railroads, which use electricity to run trains.

"The curfew will continue until the situation is under complete control," said D. Tirumala Rao, inspector general of police in Andhra Pradesh's north coastal region, where protests have been especially disruptive.

More than 100 people have been arrested over the past three days, Mr. Rao said, and 4,500 police and other security forces have been sent to the area.

For Telangana to gain statehood, the split must be approved by the Andhra Pradesh state assembly and passed by both houses of Parliament.

Opponents of splitting the state say the move would devastate what remains of Andhra Pradesh, depriving it of the current state capital of Hyderabad, a high-tech center that is the economic engine of the region.

Under the plan, Hyderabad, with its universities and other institutions, would be the joint capital for 10 years, but then would likely become capital solely of Telangana.

"There's a collective sense of disempowerment," said P. Ashok Babu, an antisplit activist. "Students and businessmen feel they will lose access to the rich resources in Hyderabad."

Farmers in areas that would belong to Andhra Pradesh also complain that they could lose out on water supplies, since the main river in the region would be largely under the jurisdiction of Telangana.

Telangana statehood supporters complain that their region, which outside of Hyderabad suffers from high poverty and unemployment, has long been neglected by Andhra Pradesh and central-government authorities.

By becoming India's 29th state, they argue, Telangana, with a population of 35 million, will get the attention and resources it needs to develop.

The statehood push, which began in the 1950s, has gained momentum recently.

After deferring action for years, the governing Congress party agreed to split Andhra Pradesh in July, in a move that political observers say is aimed at scoring points with Telangana voters ahead of national elections due by May.

Pradip Kumar Datta, professor of political science at Delhi University, said Congress is looking to "attain a short term political gain."

Chandrababu Naidu, leader of Andhra Pradesh's main opposition Telugu Desam Party, said the Congress party should have worked toward finding "a way to balance competing interests."

"What the Congress has done is immoral. It's not finding solutions but creating problems," Mr. Naidu told reporters on Monday as he began a hunger strike in New Delhi to protest the bifurcation.

Write to Vibhuti Agarwal at vibhuti.agarwal@wsj.com