The escalation in fighting in recent weeks, particularly near Donetsk airport and in the Debaltseve area, resulted in hundreds of deaths, both civilian and military, according to a new report.
The report paints a picture of "merciless devastation of civilian lives and infrastructure," said UN High Commissioner for Human Rights Zeid Ra'ad Al Hussein.
He called for all sides to adhere to the Minsk agreement, which calls for a ceasefire in many of the conflict's hotspots.
The fighting has inflicted extreme humanitarian hardship on civilians.
"Many have been trapped in conflict zones, forced to shelter in basements, with hardly any drinking water, food, heating, electricity or basic medical supplies," Zeid said in a statement
The notion that civilians remained in the conflict zone of their own will is "misguided," he said.
"Many people stay because they fear for their lives if they try to move. Many others stay to protect children, other family members, or their property. And some are forced to stay against their will, or are simply physically unable to leave," Zeid said.
A series of terror attacks in Mariupol, as well as in Kharkiv and Odesa, which are outside of the conflict zone, have set a bad precedent, he said.
"Should this trend continue, this would represent a new and very deadly chapter in this conflict, expanding the areas where the rule of law and the protection of human rights are effectively absent," Zeid said.
The UN arrived at the new estimated death toll of over 6,000 by tallying 5,809 documented deaths and assessing that many more must have been killed in recent fighting in other areas, particularly Donetsk airport and around Debaltseve.