“I don’t know if it was I who left the PD or the PD that no longer exists,” he said.
Mr Grasso added that the “real PD” was that of former leader Pier Luigi Bersani.
Deputy secretary of the PD, Mauruzio Martina, responded to Mr Grasso’s announcement on Friday by demanding respect from the former party member.
“We respect Mr Grasso and we ask for respect in turn,” he said.
“[The PD is] made up of thousands of women and men who every day, everywhere, do politics with passion and generosity for the common good.”
Mr Grasso is widely expected to join the Progressive and Democratic Movement (MDP), a splinter group from the PD led by Mr Bersani among others.
He is likely to lead a left-wing alliance formed by the MDP and other small leftist parties into the next general election, due by March 2018.