The two states that emerged from a bloody conflict in the former Yugoslavia in the 1990s will lock horns for the first time as independent nations, having been drawn alongside Belgium, Scotland, Macedonia and Wales.
"I can't be overjoyed with the draw because it's a difficult and delicately balanced group with four teams vying for just one automatic berth in the finals," Serbia coach Vladimir Petrovic told Belgrade media on Sunday.
"Apart from ourselves and Croatia, Belgium and Scotland are in with a realistic chance but Serbia is the only team in that quartet to have reached the 2010 finals in South Africa and hence we will start as favourites.
"We must not underestimate Macedonia either, while Wales are surely the strongest bottom-seeded team so every game in this group will be a real challenge.
"But the two matches with Croatia will be the pick of the lot because they are our biggest rivals and these clashes will have all the makings of a derby," said Petrovic.
His Croatia opposite number Slaven Bilic, who said earlier he would step down after Euro 2012, did not rule out the possibility of changing his mind.
"Of course the idea of being in charge of Croatia against Serbia is thrilling but right now, my only concern is to see that we qualify for the Euro 2012 finals in Poland and Ukraine," Bilic told Croatian media.
"Games like that will come to fans as much more than football for some time to come, because the atmosphere in the terraces is quite specific.
"It's a tough group and it shows why European qualifiers are the most unforgiving international competition, but there is a reason why we are the top-seeded team in our group.
"It's because we are the best team in the group and we have no reason to fear anyone, so I am confident that we can get through it and qualify," said Bilic, who steered Croatia to the Euro 2008 quarter-finals.
Europe's nine group winners will qualify automatically while the best eight runners-up will enter a two-leg play-off for the remaining four berths.
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