GENEVA (Reuters) - Syrian government forces and their allies have killed at least 85 civilians since Dec. 31 in stepped-up attacks against the besieged rebel enclave of Eastern Ghouta, the U.N. human rights chief said on Wednesday.

Conditions in the enclave, the last major rebel-held zone near Damascus and where at least 390,000 civilians have been besieged for four years, amount to a humanitarian catastrophe, Zeid Ra'ad al-Hussein said.

"Residential areas are being hit day and night by strikes from the ground and from the air, forcing civilians to hide in basements," he said in a statement.

Zeid said warring parties were obliged by law to distinguish between civilians and lawful military targets, and reports from Eastern Ghouta suggested of the attackers were flouting those principles, "raising concerns that war crimes may have been committed."

Among the dead civilians were 21 women and 30 children, Zeid said.

Backed by Russian strikes, Syrian government forces have escalated military operations against Eastern Ghouta in recent months. Russia rejects accusations that its jets have been targeting civilians.

Zeid said failure to evacuate urgent medical cases from the enclave was also against international humanitarian law.

Armed opposition groups holed up in Eastern Ghouta had also continued to fire rockets into residential areas of Damascus, which he said caused terror among the population.

A rocket landed near a bakery in Old Damascus on Jan. 4, killing a woman and injuring 13 other civilians, he said.

(Reporting by Tom Miles; Editing by Robin Pomeroy and John Stonestreet)