NEW DELHI — Huge daily demonstrations in the heart of Dhaka, the capital of Bangladesh, are upending the nation’s politics and illustrating how heavily the country’s bloody past still weighs on its present. Thousands of protesters, most of them college students and other young people, demonstrated again on Tuesday, fueled by broad public anger over a recent ruling by the country’s special war crimes tribunal that they say was too lenient.

Though the protests have been peaceful, a gunfight erupted in another part of Dhaka on Tuesday when followers of Jamaat-e-Islami, the country’s largest Islamic political party, vandalized vehicles and clashed with the police. Earlier in the day, the Bangladeshi government had rejected a request by Jamaat leaders to stage a counterprotest against the youth demonstrations.

For more than two years, the Bangladeshi government has been prosecuting defendants accused of atrocities during the country’s 1971 war of independence from Pakistan. On Feb. 5, the special tribunal hearing the cases convicted Abdul Quader Mollah, 65, now a leader of the Jamaat party, on charges of rape and mass murder and sentenced him to life in prison.

Within hours of the verdict, protesters gathered at Shahbagh, a major intersection in the center of the capital near Dhaka University. Their message was loud and clear: they thought the life sentence was too lenient, possibly the result of a political deal, and they demanded that Mr. Mollah be sentenced to death. Protesters waved torches and banners and chanted slogans like “Joy Bangla.”