BERLIN (Reuters) - German prosecutors said on Wednesday they were pressing perjury charges against Frauke Petry, former leader of the far-right Alternative for Germany (AfD), who last week quit the party and will sit in the national parliament as an independent lawmaker.

Lorenz Haase, senior public prosecutor in the eastern city of Dresden, said it was unlikely the case against Petry would proceed quickly as Dresden's regional court would need to apply to lift her immunity as a member of the national parliament.

Petry has been dogged by allegations that she lied under oath to a committee of the Saxony parliament about how the party's campaign for the 2014 election in the state was financed. She has denied the allegations.

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In August the regional parliament of the state of Saxony lifted Petry's immunity from prosecution.

But now that she is due to take up her seat in the Bundestag, the lower house of the German federal parliament, she will be granted immunity there. A majority of lawmakers in the Bundestag would have to vote to lift her immunity.

The first session of the lower house is expected to take place by Oct. 24 at the latest.

Petry, long considered the face of the anti-immigrant AfD, had for months been on the losing side of a dispute between the party's warring wings. She had advocated a more moderate course while others shifted further to the right and wanted the party to focus on a role in opposition rather than trying to govern.

Some AfD members have followed in Petry's footsteps to quit the AfD and she now plans to set up a new party.

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The AfD won 12.6 percent of the vote in the Sept. 24 federal election, making it the first far-right party to enter the Bundestag in more than half a century and the third largest parliamentary bloc.

(Reporting by Hans-Edzard Busemann; Writing by Michelle Martin; Editing by Gareth Jones)