At least 10 people were killed in clashes between the police and demonstrators, the government said, including two boys, ages 13 and 17, who were shot in the western state of Táchira. A police officer was shot in front of a school in Táchira, and a 43-year-old man was killed in Barquisimeto, the capital of Lara State, when a bullet pierced his head, according to the state prosecutor’s office.

The force of the unrest raised fears that Mr. Maduro’s efforts to consolidate power could steer the country toward deeper conflict.

The government took strong precautions to control Sunday’s vote. It outlawed protests in the days before and after, vowing tough sentences for those who disobeyed. And it barred many news outlets, including The New York Times, from entering polling stations to interview voters.

Some of those interviewed outside, where lines were short or nonexistent, said they hoped the government would use the new powers of the constituent assembly to crush the opposition, whose control of the legislature has already been weakened this year by the courts, which are aligned with the Maduro government.