VIENNA (Reuters) - Two top far-right Austrian candidates for next month's EU parliamentary elections quit on Tuesday, under fire from their own party ranks, bucking a trend of Eurosceptic parties in the ascendancy.

The co-lead candidate for the anti-immigrant Freedom Party said he had lost his party's trust after making racist comments, while the daughter of late Austrian right-wing populist leader Joerg Haider gave up on re-energizing her father's BZO party.

Far-right anti-establishment parties are expected to fare well across much of the EU in May's election, mining voter dissatisfaction with high unemployment and entrenched centrist parties seen as out of touch, and fear of immigration.

But the comments by the Freedom Party's Andreas Moelzer that the European Union's aggressive regulation made Nazi Germany look liberal by comparison and his warning the bloc could become a "conglomerate of negroes" risked alienating potential voters.

The Freedom Party (FPO) is scoring around 27 percent in Austrian national opinion polls, ahead of the governing Social Democrats and conservative People's Party.

But how to handle Moelzer had become a tricky test for the party, which treads a fine line in positioning itself as a mainstream party electable by voters fed up with creeping EU centralization but who would not see themselves as far-right.

Pressure had mounted on the party's leadership to fire the 61-year-old veteran EU parliamentarian, who was supposed to be one of its two top candidates.

Moelzer told the Austria Press Agency he was not prompted to quit by pressure from other political parties, the media or other external critics. "It is the obvious loss of confidence in my party that prompts me to do this," he said.

HAIDER'S CHARISMA

The daughter of Joerg Haider also quit as the BZO's top candidate for the EU polls after less than a month of campaigning, citing criticism from within the movement's ranks.

Ulrike Haider-Quercia, a university professor in Rome, had hoped to recapture her father's charisma and political acumen for the floundering Alliance for the Future of Austria (BZO), which has been polling only around 2.0 percent in opinion surveys.

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Joerg Haider, who helped bring anti-immigrant politics into the European mainstream, created the right-liberal BZO after quitting the far-right Freedom Party he had previously led. The BZO's popularity has dwindled since his death in 2008 car crash.

His daughter told the Austria Press Agency (APA) she could not follow her own political line in the face of party critics.

"Criticism was raised against my pro-European positions and my views on security policy in Europe. Therefore, I am no longer available as lead candidate for the BZO list," the 37-year-old wrote in an email to APA.

BZO leader Gerald Grosz said in a statement: "I am naturally disappointed in the step taken by Dr Ulrike Haider-Quercia, although I can only respect and understand her withdrawal from the candidacy."

Separately, the pro-business party created by Austro-Canadian billionaire and Magna International founder Frank Stronach said it would not run for the EU parliament.

Team Stronach leader Kathrin Nachbaur said the party, which scored a disappointing 6.0 percent in last year's Austrian elections, needed to concentrate on coming provincial and national polls.

"One has to be realistic. I know our polling scores. For us it is important to use our resources in a sensible way. The EU parliament is in any case a toothless apparatus," she told Der Standard newspaper in an interview for Wednesday's edition.

(Reporting by Michael Shields and Georgina Prodhan; editing by Ralph Boulton)