Local news media reported three demonstrators were killed in Jakarta, but there was no confirmation from authorities or local hospitals.
The protesters claim the new law will strengthen the military's already powerful role in domestic politics, and threaten the giant country's move toward democracy.
Police fired rubber bullets and beat students with clubs in two Jakarta protests, injuring dozens of demonstrators.
Four were rushed to the hospital with bullet wounds, while other bloody protesters were pulled away from the scene by friends.
An estimated 6,000 students and their supporters, many carrying sticks, clashed with police outside parliament, starting early in the afternoon and going into the evening. Police also fired tear gas into a sea of angry demonstrators, who set several vehicles on fire.
At least five police officers were burned when they were hit by firebombs in Jakarta.
Four-thousand protesters flooded into the streets in the country's second-largest city, Surabaya, and more than 200 rallied on the resort island of Bali.
Just hours earlier Thursday, Indonesia's parliament unanimously approved the law giving the armed forces wide-ranging emergency powers, triggering the violent reaction.
The measure allows the military to ban protests, take over the telecommunications system and mail service, and curb freedom of expression if a state of emergency is proclaimed. Even before the new law, the military held a dominant role in governing this country of 210 million people.
Â"The bill will be enacted not to serve the interests of the military but to safeguard the unity of the nation,Â" said Gen. Wiranto, head of the Indonesian armed forces and a key national figure.
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