Barroso said in a statement to Croatia: "I hope that your government will take the measures necessary early in its mandate to address these and other issues of importance in the EU accession process."
Italy and Slovenia say that when Croatia sought EU candidacy in 2004, Zagreb had agreed to allow exemptions for EU countries in the zone until a fishing accord was finalised with Brussels.
EU officials have warned Croatia that failure to reach a deal on the zone could derail its plans to complete accession talks by mid-2009.
Sanader said Croatia would soon propose talks on the issue.
Speaking on Monday, he said: "Croatia will propose a meeting with representatives of Slovenia, Italy and the European commission to find a common solution."
'Matter of urgency'
A spokeswoman for Olli Rehn, enlargement commissioner, said the new government should tackle the issue as a matter of urgency.
Croatia created the zone, which extends its jurisdiction beyond territorial waters to the middle of the Adriatic, because it said it needed to preserve fish stocks and limit pollution.
Its fishermen say Italy's better-equipped fleet could deplete fish stocks on the Croatian side of the Adriatic after doing so on its side.
They said Italian trawlers often fish illegally in Croatian territorial waters.
Barroso also stressed the need for Croatia to make progress in reform of the judiciary and public administration, fighting corruption, the return of refugees and economic restructuring.
Sanader won parliament's backing on Saturday for a proposed centre-right coalition cabinet after an inconclusive November 25 election, but political analysts say it faces an uphill task in speeding up EU membership talks.