Ignazio Marino made the announcement after meeting investigators.
Earlier this week, the authorities announced the arrest of 37 suspects and said they were investigating 100 more.
Those arrested are suspected of fraud and money-laundering in connection with public works.
Among those under investigation is Rome's former mayor Gianni Alemanno.
He denies wrongdoing, but has resigned from his position in the right-wing Brothers of Italy-National Alliance party while investigations continue.
One of those arrested was Massimo Carminati, the former leader of a far-right armed group.
Police seized assets worth 200m euros (Â£159m; $258m) in the operation.
Prosecutors allege that criminal gangs conspired with politicians to steal funds intended for migrant and refugee centres.
"Drug trafficking is not as profitable," one member of the network was recorded as saying in a wire-tap.
The state authorities have said that they may take over the running of the city.
The Chief Prosecutor, Giuseppe Pignatone, said: "We have answered the question as to whether or not the Mafia exists in Rome - it certainly does."
The mayor of Rome has ordered a review of all city contracts after an investigation uncovered a suspected criminal network involving some of the city's politicians.