* Former judge rejected by opposition
* EU watching closely
* Albanian politics marked by bitter confrontation
By Benet Koleka
TIRANA, May 30 (Reuters) - Albania's parliament failed to elect a president at the first time of asking on Wednesday, dogged by factional rivalry over the largely ceremonial post.
The president is supposed to be a figure of national unity elected by consensus in parliament, but the opposition has accused the ruling Democratic Party of trying to push through the appointment of Zhezair Zaganjori without consulting it.
On Wednesday morning, the Democrat-led bloc in parliament proposed the former Constitutional Court judge and ambassador to replace outgoing President Bamir Topi for the next five years, as Topi's fixed term expires.
The opposition Socialist Party made clear he was unacceptable. The first-round session expired without a vote, meaning the process moved straight to a second round.
In the first three rounds a winner must achieve a three-fifths majority. If that fails, the bar drops to a simple majority of 71 votes in rounds four and five.
The government of Prime Minister Sali Berisha, head of the Democratic Party, holds a majority, but forcing through a president in the fourth or fifth rounds opens the door to opposition complaints of being railroaded.
"I urge all political parties to pursue a spirit of acceptance, and then the solution will come in the second or third round," said parliament speaker Jozefina Topalli.
Topalli asked party leaders to agree on a date for the next vote. The process could take several days.
Since emerging in 1991 from decades of isolation and communist dictatorship, politics in the impoverished Balkan country has been marked by bitter confrontation between the two main blocs, the Socialists and the Democrats.
The rivalry has slowed reform and kept Albania firmly behind Balkan neighbours Serbia, Montenegro and Macedonia in the queue to join the European Union.
The EU is pressing Albania to show more democratic maturity before it makes the country of 2.8 million people an official candidate for membership, having twice turned it down in the past two years.
After opposition protests erupted into violence last year, the EU urged Albania to overhaul its electoral system before voting for a president, but parties have yet to agree how.
Though largely a ceremonial figure, the president has the power to hold up legislation and appoints the prosecutor general and the head of the Albanian secret service. (Editing by Matt Robinson and Andrew Roche)