Croatian Prime Minister Zoran Milanovic should be celebrating his country becoming the 28th EU member on Monday.
But the occasion looks set to be overshadowed by an extradition row with Germany.
Zagreb has refused to hand over an alleged ex-spy to Berlin wanted in connection with a communist-era assassination in what was West Germany.
Josip Perkovic is wanted in connection with the killing 20 years ago of Stjepan Djurekovic, an exiled Croatian dissident.
Croatia will not be bound by the EU arrest warrant until Monday, but the government has proposed changing the law to exclude handing over its citizens for crimes committed before August 2002.
Croatia’s neighbour, Serbia, has moved closer towards EU membership.
On Friday, Brussels gave the green to opening talks with Belgrade by January at the latest.
That decision comes after protracted negotiations between Serbia and Kosovo to normalise ties.
It was a key condition demanded by the EU before even considering Serbia for membership.
Leaders also plan an association agreement with Kosovo, a step towards eventually joining the bloc that comes with economic benefits.
Pristina broke away from Belgrade at the end of a year-long war in 1999, declaring its independence in 200