Duplessis spoke this morning at Laval City Hall, addressing the details of the complaint which were reported by several media outlets yesterday.
"I never solicited, I never received anything of a sexual nature," he said. "I never received [anything] of a sexual nature and I never received favours of a sexual nature."
Laval has called an emergency council meeting for 4 p.m. ET today.
Quebec provincial police confirmed they are looking into a complaint about extortion, but would not discuss details.
Police sources told Radio-Canada that the allegation involves an incident that happened on June 14. Duplessis allegedly requested the service of a prostitute, who went to his chalet accompanied by a female driver. One of the two women recognized him, and Duplessis allegedly cancelled the encounter without paying them.
The women insisted on being paid and made three attempts to collect the money.
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Duplessis filed a complaint with Quebec provincial police, a fact he confirmed this morning without addressing the details or circumstances or relationship he had with the accused.
He also said an arrest had been made in the case.
Duplessis said he will not resign in the wake of the latest scandal at Laval City Hall, which has been plagued by corruption investigation raids and resignations in recent months.
"I will continue my work as mayor," he said. "I will continue my work for the citizens of Laval. I will not resign over this extortion threat."
Duplessis was elected interim mayor in November after long-time mayor Gilles Vaillancourt resigned under a cloud of corruption allegations.
Vaillancourt was later arrested and charged with a number of offences including gangsterism. He has maintained his innocence.
The entire 21-member council was at one time part of Vaillancourt's Parti PRO des Lavallois. The party was dissolved after the former mayor's resignation and some council seats are now vacant.
Duplessis and others from the party were recently implicated in testimony before the province's corruption commission.
Jean Bertrand, the former official agent for the PRO des Lavallois party, told the commission that the interim mayor and others at city hall along knowingly accepted illegal payments to cover campaign contributions.
He told the commission that every member of Laval's executive committee, and almost every elected official in the mayor's party, took cash that came from colluding engineering companies in the late 1990s and early 2000s.
Bertrand is currently facing criminal charges and was arrested in the same police sweep that saw charges laid against Vaillancourt.
Duplessis is not facing any charges based on the allegations made before the commission.