Rockets slammed into a high-security prison on Monday in the rebel-held city of Donetsk, igniting a riot that allowed more than 100 prisoners to flee, authorities in eastern Ukraine said.

Donetsk city council spokesman Maxim Rovinsky said a direct rocket hit killed at least one inmate and left three others severely wounded. In the chaos, he said 106 prisoners escaped, included some jailed for murder, robbery and rape.

In the past week Ukrainian government forces have intensified their military operations and surrounded Donetsk, the largest city in rebel-held eastern Ukraine. Exchanges of rocket fire and deaths from shelling have become a feature of daily life and hundreds of thousands have chosen to flee.

The prison break became possible after a substation providing the building with electricity was damaged, disabling the facility’s alarm system.

“Extremely dangerous prisoners are now free. It is hard to know the extent of threat this poses to the city, which is flooded with weapons,” Mr. Rovinsky said.

Officials with Ukraine’s state penitentiary service said later Monday that 34 prisoners had returned to the jail. It was not immediately possible to verify that claim.

Both Ukrainian government forces and the pro-Russian rebels who want independence for their eastern region have deployed heavy and often imprecise weapons in the battle that began in April. Apartments and other civilian buildings have frequently been hit, adding to the mounting death toll among civilians.

Mr. Rovinsky said on Monday at least 10 homes, shops and garages were hit by overnight rockets. He added that 20,000 people had no electricity in Donetsk and an estimated 400,000 have fled the city, which had a pre-war population of 1 million. Many shops have closed and supplies are dwindling at the few still open.

The Ukrainian Army’s strategy has focused on encircling Donetsk and nearby rebel towns and breaking off road links with other separatist towns and villages further east, closer to the Russian border.

Many of those in Russian-speaking eastern Ukraine distrust the new central government in Kiev, which came to power after the February ouster of former President Viktor Yanukovych, whose power base was in eastern Ukraine.

Fighting began a month after Russia annexed Ukraine’s peninsula of Crimea in March.