The Tribune de Geneve newspaper quoted justice ministry spokesman Henri Della Casa as saying that authorities had decided to open a formal criminal inquiry into allegations that Ramadan raped a woman in a Geneva hotel in 2008.
"I confirm the opening of an inquiry," the paper quoted Della Casa as saying, a key step that indicated the authorities believed the allegations merit further investigation.
The accuser lodged her complaint in April.
Islamic scholar Tariq Ramadan 'paid woman for silence'
"The prosecutors and Geneva police have worked quickly and worked well," Romain Jordan, the lawyer representing Ramadan's Swiss accuser, told AFP in an email.
He described the decision to open a criminal inquiry as "a major advance" that "demonstrates the seriousness of the allegations made by our client."
Ramadan, a Swiss citizen and Oxford University professor whose grandfather founded Egypt's Muslim Brotherhood movement, has not yet been interviewed by Swiss prosecutors.
Islamic scholar Tariq Ramadan to face French judge in rape, assault case
Jordan said that following the opening of a criminal case, Swiss investigators will now have to travel to France to hear Ramadan's side of the alleged rape.
The 56-year-old scholar, a prominent and controversial figure within Islam, has denied criminal wrongdoing in connection with the French charges and insisted that all relations with his two accusers were fully consensual.
Earlier this year, French judges dismissed a third rape allegation against Ramadan by a French Muslim woman who accused him of raping her nine times between 2013 and 2014.
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