Serbia, Croatia and Bosnia, fought a series of brutal wars from 1992 to 1995 as the nation of Yugoslavia broke apart.
The apology is aimed at showing the European Union that Serbia is addressing the painful legacy of the rule of Slobodan Milosevic, then Serb president, as it seeks to join the bloc.
"The Srebrenica resolution is necessary to discuss in parliament because with this Serbia wants to demonstrate our desire to move to regional reconciliation and demonstrate good neighbourly relations among the countries in the region," Mirko Cvetkovic, Serbia's prime minister, said last week.
Parliament is expected to vote on the resolution, which also urges other former Yugoslav countries to pass motions condemning crimes against the Serbs, later on Tuesday.
In the months preceding the end of the war, Bosnian Serb forces led by Ratko Maldic committed the massacre, the worst killing since the second world war.
Mladic is still at large, but the EU has made his capture one of the conditions for Serbia to progress in their accession to the grouping.
In 2009, a European parliament resolution condemned the Srebrenica massacre as genocide and called on the region to commemorate its July anniversary.