MOSCOW — The senior official in charge of prisons in Georgia resigned on Wednesday, after a television station broadcast graphic video of prison inmates being brutally beaten and sodomized by guards.

As hundreds of people took to the streets to protest on Wednesday, President Mikheil Saakashvili quickly condemned the abuses and promised that those responsible would be prosecuted. Mr. Saakashvili also pledged to overhaul the prison system.

The prosecutor general’s office said that 10 guards and other prison officials were arrested as part of an investigation into cases of “torture and inhuman and degrading treatment” and that charges had been filed against one additional prison inspector who was being sought by the police. A number of officials resigned, including Khatuna Kalmakhelidze, the country’s 33-year-old minister of corrections and legal assistance.

“What happened in the Gldani Number 8 penitentiary facility is a horrific affront to human rights and human dignity,” Mr. Saakashvili said in a televised statement, several hours after the abuses were broadcast on TV9, an opposition channel. “Those who organized, committed and allowed these crimes to happen will be severely punished.”