The council is joining other local authorities across the UK by publishing a statement of support on its website.
During the Srebrenica Genocide in Bosnia and Herzegovina in July 1995, 8,372 victims were killed.
Provost Jean Jones said: “More than 8000 Muslim men and boys were killed over a few days in mainland Europe. It is awful to think this happened in our lifetime and we have to ensure this never happens again.
“It is now more important than ever for us to come together, no matter what our background, to celebrate diversity and to stand together against discrimination. By learning from the lessons of the past, we can create a safer, better future.”
The charity Remembering Srebrenica was founded in 2013 and raises awareness of the genocide in the UK. It organises the UK Srebrenica Memorial Week, which leads up to the EU-wide day of remembrance
Remembering Srebrenica Chairman Dr Waqar Azmi OBE said: “This was the single greatest atrocity committed on European soil since the Second World War and a brutal reminder of man’s inhumanity to man.
“I look forward to seeing councils across Britain work with local people to take actions that help to tackle hatred and build stronger, more cohesive communities whilst ensuring that the lessons from Srebrenica are never forgotten.”
The massacre has also been commemorated by a work of art (pictured) by leading Scots painter Peter Howson.
A former war artist in Bosnia who has spoken frankly about his trauma over what he witnessed there , Mr Howson unveiled the painting last December for Glasgow Museums.
Mr Howson said at the time: “It is difficult to put into words the horror of the massacre of over 8,000 men and boys in the town of Srebrenica during the Bosnian civil war.
“The experience caused me many years of illness and the breakup of my family.
“I still have memories too painful to talk about, but I find that painting these terrible events helps me to try and understand why we do such evil things to each other.
“This painting records a moment in European history; a memory in my mind’s eye of what happened that day.’