Ilaria Salis, 39, was a candidate of Italy's small Greens and Left Alliance (AVS) party in the European Parliament elections, which received 6.7 percent of the vote at the weekend.
The case of Salis was front-page news in Italy earlier this year after she appeared in a Budapest court handcuffed and chained with her feet shackled.
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After being imprisoned for more than a year, Salis was given house arrest last month following an appeals court decision.
Her defence team said her election to the EU Parliament means that she can ask for immunity, however.
"We have had six MEPs elected, and among these is Ilaria Salis," Nicola Fratoianni, one of the party's leaders, told a press conference Monday.
"Now we want Ilaria here in Italy - free, and with immunity, ready to carry out her mandate".
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Salis's lawyer told Italy's Il Messaggero daily his team may request immunity before July 16th.
"We now have to wait for a formal step in which Ilaria will be proclaimed a parliamentarian. Once this step has been taken, we will make a request to the Hungarian judges for her release, because Ilaria has the right to parliamentary immunity," said lawyer Eugenio Losco.
EU law provides for "exemption from any form of detention and suspension of criminal proceedings" for parliamentarians, he said.
Salis, a teacher from Monza, near Milan, was arrested in Budapest in February 2023 following a counter-demonstration against a neo-Nazi rally.
She risks an 11-year jail sentence after being charged with three counts of attempted assault and accused of being part of an extreme left-wing organisation.
Her trial began last month.
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