Josipović said negotiations are better for Croatia than a recently adopted law that seeks to void war crimes indictments sent from Serbia, the Croatian agency HINA reported.
The law was drafted hastily after Serbia issued indictments for war crimes against Croatian nationals, including prominent political figures such as Vladimir Šeks, the former speaker of parliament and member of the centre-right HDZ party that governs Croatia.
The European Commission had called for ''prudence'' and ''careful consideration'' with regard to the Croatia government's push to pass the bill earlier this month.
Josipović said on Monday a bilateral agreement would put an end to further groundless prosecutions of Croatian war veterans and enable the continuation of cooperation in dealing with war crimes.
"I call on the [Croatian] government to embark on that together," Josipović is quoted as saying, reiterating that the new law harmed Croatia as it did not prevent situations in which war veterans could be prosecuted without probable cause.
Josipović, a Social Democrat, is at odds with Prime Minister Jadranka Kosor, the HDZ leader, in advance of parliamentary elections due in December.
Explaining that he would request the Constitutional Court to review the new law, Josipović argued that it undermines cooperation between Croatian and Serbian prosecutors which he described as good. Josipović said that the measure could also damage relations between Croatia and Serbia, adding that Brussels was in doubt whether Zagreb was serious about strengthening the rule of law.
Croatia has concluded its EU accession negotiations, but is being monitored for progress in law enforcement until its accession, expected on 1 July 2013. The accession treaty is expected to be signed on 19 December in Warsaw.
Josipović said he would call the elections after consultations with the parliamentary parties, adding that he might announce the date on Friday.