The resolution expressed sympathy for the victims and offered an apology for not doing enough to prevent the massacre, but stopped short of calling the killings "genocide".
The ruling coalition of pro-Western Democrats and Socialists hopes to win EU and investors' favour with the measure, which was adopted after a live TV debate of nearly 13 hours, which ended after midnight.
"We are taking a civilised step of politically-responsible people, based on political conviction, for the war crime that happened in Srebrenica," said Branko Ruzic, whose socialist party was led by strongman Slobodan Milosevic during the 1990s.
Bosnian Serb forces led by General Ratko Mladic killed about 8,000 Bosnian Muslim men and boys after taking over the eastern enclave that was put under the UN protection. The massacre is Europe's worst atrocity since World War Two.
One Western diplomat stationed in Bosnia when the Srebrenica massacre occurred said passing the resolution without arresting Mladic meant little.
"As a substitute, it's offensive, it's an insult. Done in tandem with a legal step, then it's significant," the diplomat said. "If they think they can let Mladic run free for another 15 years, it's a grave injustice."
Belgrade applied for European Union membership in December but must capture and send Mladic to the war crimes tribunal in The Hague before starting talks. The former general, hailed as a hero by many Serbs, is believed to be hiding in Serbia.
Supporters, opponents raise voices
For some parliamentarians, the resolution was unjust for ignoring war crimes against Serbs.
In Srebrenica "the crime was no greater than in other places," said opposition MP Velimir Ilic, citing neighbouring Croatia's moves against Serbs during the war. "We can't put everything else off to the side."
Others, such as Cedomir Jovanovic of a liberal opposition party, criticised it for not deeming Srebrenica genocide.
"We wanted a completely different resolution but apparently that is not possible," he told the parliament. "Our society does not have the sufficient strength."
Dozens protested in front of the parliament, some carrying pictures of Mladic and Bosnian Serb wartime leader Radovan Karadzic, who is on trial in The Hague for the Srebrenica genocide.
Another group carried small signs saying "Srebrenica was not in my name".
Prime Minister Mirko Cvetkovic told Reuters last week the resolution should help improve strained ties with Bosnia.
"Srebrenica for us is an event that in the long run should open the door for future cooperation," he said.
Yet many in Bosnia, where 100,000 died during the 1992-95 war, found the Serbian resolution too little, too late.
"Many criminals who slaughtered and killed our children fled to Serbia where they live as free citizens and enjoy full rights," said Munira Subasic, the head of a Srebrenica women's association who lost her son and husband at Srebrenica.
"There is no apology for the crimes. Justice can only be served once all the criminals responsible for the atrocity are named and held accountable," she told Reuters Television.
(EurActiv with Reuters.)
