The SDP and the Istrian Democratic Party (IDS) supported the motion while the Croatian Democratic Union (HDZ) and the Croatian Party of Rights (HSP) were strongly against it.
Mato Arlovic of the SDP said that the equation of those rights would be a civilisational step forward and it could also redress injustice inflicted on NOB invalids who enjoyed fewer rights than disabled veterans of the Homeland Defence War.
Josip Djakic of the HDZ described the motion as frivolous, stressing that the sponsors failed to propose funds for the implementation of such a law.
HSP MPs were against the equation of laws, with Pero Kovacevic saying that it was high time that claims that the contemporary Croatian state was based on anti-fascism stopped. "It was Croatian Homeland Defence War veterans and not anti-fascism who established Croatia," Kovacevic said.
MPs continued the debate despite frequent appeals by the chairman, Luka Bebic, to refrain from historical topics.
Some MPs who were against the motion accused the SDP of trying to cover up crimes committed by Tito's partisans at the end of the Second World War.
Bebic reminded deputies that the motion was about the disabled veterans and not about who fought on which side.
The Croatian Sabor wrapped up today's sitting with a debate on a draft bill on the Coast Guard. The debate on this bill, proposed by the SDP, will resume on Wednesday.
Also on Wednesday, the Sabor will commemorate Parliament Day in memory of 30 May 1990 when the first multi-party Croatian parliament was inaugurated. The ceremony marking this event is due to begin in Parliament at 19:00 hours.