CAIRO — At least 13 people were killed as violence broke out during Muslim Brotherhood marches in several Egyptian cities on Friday, health officials said, in the deadliest day of clashes in months.

The victims included protesters — one an 18-year-old college sophomore — and, apparently, bystanders. Brotherhood supporters said riot police officers had fired on their marches without provocation in some places, while the authorities said they had seized weapons from demonstrators. Dozens of people sustained gunshot and other injuries in violence that was the latest blow to the military-backed government, which is trying to impose stability just 10 days before Egyptians are set to vote on a draft constitution.

Six months after the army’s ouster of President Mohamed Morsi, a Brotherhood leader, the grinding civil conflict between Mr. Morsi’s supporters and the government appears to be reaching another peak.

The authorities are desperate to hold the constitutional referendum, seeing it as a chance to quiet unrest by marginalizing the Brotherhood with a public show of support for the government-sponsored charter.