UN human rights spokeswoman Cecile Pouilly said: "This corresponds to a clear escalating trend."
On average, more than 60 people a day have been killed or wounded since fighting began in mid-April in eastern Ukraine, rising to at least 70 people a day in the first week of August, she said.
Nearly 5,000 have been wounded to date. The figures for casualties include Ukrainian soldiers, armed groups, pro-Russian militants and civilians, but are "very conservative estimates", Ms Pouilly said.
"For instance, civilian casualties are likely to be under reported, due to the continuing insecurity which prevents affected people from getting access to medical aid and because communication channels have been disrupted."
It was not clear whether Russian soldiers were included in the UN estimates for casualties which were based on information received from Ukrainian authorities as well as local medical facilities, Ms Pouilly said.
In fresh clashes yesterday, 12 people were killed when a bus belonging to the Ukrainian Right Sector party came under fire from pro-Russian forces and at least three people were killed in the separatist-controlled city of Donetsk as the Kiev government intensifies its shelling campaign.
Residents said the intermittent artillery barrage lasted about two hours. One high-rise building appeared to have been struck five times and two bodies were seen lying in the street.