Applebaum called a news conference today to address the report, published in newspaper Le Devoir, that he was at Montreal restaurant La Cantina in 2003.
The restaurant had a reputation for being a hangout for members of the Rizzuto clan.
In 2009, the restaurants' owner, Frederico Del Peschio, was shot to death in the parking lot.
Today, Applebaum said he is a man of integrity and transparency who has nothing to hide.
He admitted to being at the restaurant, but said at the time he had no idea about its links to the Mob. Applebaum said he never returned to the restaurant once he learned of those ties.
"I am not afraid of the mafia. I do not hang out with the mafia, and I do not know the mafia," he said.
Applebaum said he has nothing to apologize for.
The mayor said he has never accepted money or gifts in return for political favours.
He said his main goal is to restore Montrealers' confidence in their government.