* Main parties bidding for outright parliamentary majority
* Election seen as gauge of democratic credentials
* Next government faces judicial reforms targeting graft (Updates with party leaders voting, turnout, police statement)
TIRANA, June 25 (Reuters) - Albanians were voting in a parliamentary election on Sunday with the ruling Socialists and rival Democrats seeking a majority to push through judicial reforms vital for membership of the European Union.
The race pits Socialist Prime Minister Edi Rama against the centre-right Democratic Party of Lulzim Basha. Neither party won the 70 seats needed for a majority in the 2013 or 2009 election.
Polls opened at 7 a.m. (0500 GMT) on what is forecast to be the hottest day of the year so far with temperatures reaching 39 degrees Celsius. They close at 7 p.m.
The elderly and the young were up early to vote when polling stations opened in Tirana, to avoid the heat or to head to the beach after voting. Turnout at 1 p.m. was 27.28 percent.
Thousands of Muslims, who make up 60 percent of the population, recited prayers in the newly-built pedestrian square in central Tirana early on Sunday to mark the end of Ramadan.
Exit poll results are expected shortly after polls close, with the first official results due on Monday.
The vote will be watched closely by Albania's European neighbours, keen for it to leave behind a history of election irregularities and violence.
"I expect a radical change, a better future for the Albanians so they dont emigrate throughout the world," Tirana resident Petrit Sulo said after casting his ballot.
Campaigning has been mainly peaceful after a pact by the two main rivals that sought to guarantee a trouble-free election.
Both main parties want to ditch the Socialist Integration Movement (SIM) of president-elect Ilir Meta, which gained the role of king-maker by propping up their respective governments for the last eight years.
"I am full of confidence this will be a beautiful day for Albania," Rama said after casting his ballot.
The Interior Ministry said in a statement hundreds of cases of vote buying and intimidation of voters had been reported, but did not give more details on the political parties involved in those incidents.
'FACADES AND PALM TREES'
Opinion polls give Rama's Socialists the edge over the Democrats, but it is not clear whether he could garner enough support to win an outright majority.
The two frontrunners have said they will jointly ask the European Union to advance towards accession. They have not said whether they might rule together in coalition.
Since taking office, the Socialists have improved tax collection and boosted the performance of the electricity sector. Economic growth accelerated to 3.45 percent last year, compared with 0.97 percent in 2013.
But they failed to fulfil promises to create 300,000 new jobs and secure free health care for everyone aged over 40. The country's international reputation was tarnished by data showing Albania had become Europe's biggest open-air cannabis producer.
Basha, a foreign-educated former transport and interior minister, accuses Rama of glossing over Albania's problems with "facades and palm trees" and says he has neglected the economy.
Implementing a sweeping judicial reform aimed at rooting out widespread graft will be a priority for the next government as it seeks progress towards joining the European Union.
"This is the chance to do something to change the country. It is a hot day but it is the day when you decide for the next four years for yourself and your families," Basha said after casting his vote.
Rama said last month the Balkan country could get a green light for formal talks to start at the end of this year. (Reporting by Benet Koleka and Ivana Sekularac. Editing by Jane Merriman)