The European Commission Against Racism and Intolerance (ECRI) published its annual report on Serbia and also said hate speech and hate crime were on the increase in the Balkan state.
It said Belgrade should “actively implement” a strategy to punish those guilty of war crimes.
About 8,000 Bosnian Muslim men and boys were killed when the Bosnian Serb army attacked the UN ‘safe area’ of Srebrenica in July 1995, despite the presence of Dutch troops tasked with acting as UN peacekeepers.
A total of 8,400 people also remain missing since the end of the 1992-1995 Bosnian War, according to the Institute for Missing Persons in Bosnia and Herzegovina.
Serbia's parliament in 2010 adopted a resolution condemning the Srebrenica massacres, but failed to define the crime as genocide.
On Tuesday, ECRI chair Christian Ahlund said "political leaders should formally acknowledge the genocide of Srebrenica".
However, it was only in February this year that the first Srebrenica trial opened in Belgrade -- 22 years after the killings.
Eight former members of a Bosnian Serb special police unit were accused of organizing and participating in the murder of more than 1,300 Bosnian civilians in the Kravica municipality near Srebrenica.
The killings in Kravica were among several massacres committed during the Srebrenica genocide; the victims were later found in several mass graves.
In April, former Serbian chief war crimes prosecutor Vladimir Vukcevic also said what happened in Srebrenica should be described as genocide.
Speaking at a panel discussion in Belgrade, Vukcevic said politicians were playing political games with the facts about the killings.
The Serbian parliament eventually chose a new chief war crimes prosecutor on May 15, more than a year after Vukcevic's term expired in December 2015.
Serbian Prime Minister and current president-elect Aleksandar Vucic attended the 20th anniversary of the Srebrenica genocide in 2015.
Amid emotional scenes, he was forced to flee the ceremony after his party was attacked with stones and sticks.