GENEVA — Fighting in eastern Ukraine has eased recently, but at least 6,417 people have died in the conflict and abuses that may amount to war crimes continue to be committed by both sides, the United Nations said Monday.

Nearly 16,000 people have also been injured since fighting broke out between Ukraine and pro-Russian separatists in the region in April 2014, Ivan Simonovic, assistant head of the United Nations human rights office, told reporters in Geneva in presenting the latest report of its monitors.

The casualty estimates were conservative, Mr. Simonovic emphasized. Both sides have reported that hundreds of people are missing, and morgues in the contested areas reportedly hold hundreds more bodies, the report said.

Indiscriminate shelling and the number of civilian casualties from the fighting have fallen since February, but “the shelling has not stopped, nor have armed hostilities between Ukrainian armed forces and armed groups, meaning that civilians continue to live in fear,” the human rights office said in a statement released with its report, which focuses on developments in the three months to May 15.