"Crimes such as the crime in Srebrenica must immediately be condemned and criminals, who are not heroes but killers, should be immediately brought before justice so that we can find our inner peace and safeguard the principles of the human justice," Marovic told the Tanjug news agency.
Marovic said that he, personally and as a Montenegrin and as the President of Serbia-Montenegro, "feels shame and sadness over that crimes".
"Serbia and Montenegro are suffering due to that (crime), although citizens of Serbia and Montenegro have never authorised or backed anybody to kill innocent people," according to Marovic's statement, which was also carried by Wednesday's issue of the Belgrade-based Blic newspaper.
Marovic said that Serbs were not a criminal people but they "must condemn the Srebrenica crime, no matter where they are living, as that crime was committed by concrete criminals and not the Serb people".
On Tuesday, the Serbian parliament failed to reach consensus on a text of a declaration with which Serbian MPs were to deplore the 1995 Srebrenica massacre.
Serb troops killed close to 8,000 Muslims in Srebrenica, eastern Bosnia-Herzegovina, in July 1995, after they overran that area which was until than a UN safe haven.