The allegations come from a Belgian prostitute who said she was at a hotel sex party in the city in December 2010.
Former IMF head Dominique Strauss-Kahn, 63, is already under investigation with three other men over their alleged roles in a prostitution ring. He denies the allegations.
A charge that he attempted to rape a US hotel maid was dropped last year.
But the case put an end to DSK’s career at the International Monetary Fund and dashed his hopes of running as Socialist candidate for the French presidency.
In March, prosecutors in the northern French city of Lille placed him under formal investigation in connection with what has become known as the Carlton affair, after the Lille hotel in which several orgies are alleged to have taken place.
Businessmen Fabrice Paszkowski and David Roquet and policeman Jean-Christophe Lagarde, who were named with DSK as part of the Carlton affair, have also been implicated in the Washington hotel investigation.
It is claimed that the men hired prostitutes for sex parties in France and the United States while DSK was in charge of the IMF.
According to a statement from the Lille prosecutor, the investigation centres on an incident “that could be described as gang rape”.
The allegations are said to have come to light from evidence given by a Belgian prostitute who told Belgian police that she was forced into certain acts of non-consensual sex while in Washington on 16 December 2010. She has not filed a complaint.
“I didn’t scream but I said clearly and loudly that I didn’t want to,” the woman is said to have testified.
But a second Belgian prostitute has called her account of events into question, in an interview with French media.
Police in Washington say they have checked their records for 16 December at the city’s W hotel, named by media as the hotel involved, and have found no reports detailing allegations of such activity.
Earlier this month, the former IMF managing director’s lawyers denied the accusations against him, saying he was the victim of a “lynching campaign”.
The initial charge of “aggravated pimping as part an organized gang” carries a potential prison term of 20 years. A rape conviction can prompt a similar sentence.
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