Marino has denied allegations he paid personal restaurant bills using official funds.
He offered to pay back EUR 20,000 ($22,500) early on Thursday but later said he would stand down, when his Democratic Party withdrew its support, the report says.
Marino was already under pressure over the dilapidated state of Italy's capital.
The mayor faced calls to resign last year for a series of unpaid parking tickets, and saw his popularity slump after a corruption scandal implicated several politicians, including his predecessor.
Marino, who took office in 2013, was also criticized for not stopping an alleged mafia boss being given a glitzy funeral in the city.
He said his resignation should not be taken as an admission of guilt, but said "political conditions" had made it impossible to continue.
