Since February, large-scale demonstrations have been held in response to decisions of the Bangladeshi International Crimes Tribunal, which was established in 2010 to try people accused of committing atrocities, including genocide, war crimes and crimes against humanity during the 1971 war.
In recent weeks, 88 people have been killed and hundreds injured in clashes between security forces and activists, the independent experts said in a release.
"I call upon the authorities in Bangladesh to ensure prompt, impartial and effective investigations of all killings committed irrespective of whether they were committed by a state or a non-state actor," said Christof Heyns, the special rapporteur on extrajudicial executions.
The U.N. Human Rights Council, which has headquarters in Geneva, also indicated there have been "worrying reports on attacks against members of the Hindu community, their homes and places of worship, as well as against journalists."
Pablo de Greiff, special rapporteur on the promotion of truth and justice, said, "Governments should strive to achieve justice for victims of past human rights violations and restore trust in the rule of law including through criminal prosecutions."
In February, U.N. independent experts had expressed concern about possible non-compliance with fair trial and due process during tribunal proceedings, including the imposition of death sentences.
The unpaid independent experts, or special rapporteurs, are appointed by the U.N. Human Rights Council to examine and report on specific human rights themes.
Notable deaths of 2014 [PHOTOS]