"I am shocked and horrified," said Lorenzo Guerini, the deputy head of the party.
Renzi quit as prime minister in December after losing a referendum on constitutional reform but is eager to return to power and is pushing for national elections to be held this year rather than early 2018 as scheduled.
This has angered the PD dissenters, who argue that more time is needed to work out the party's problems and to develop a manifesto that promotes welfare spending and tackles inequality -- areas that they say the PD-dominated government has ignored.
PD officials are due to decide on Tuesday when to hold the leadership ballot. Any move towards a swift vote would bolster Renzi's quest for early elections and make a schism more likely.
Recent opinion polls have put the PD neck and neck with the 5-Star Movement, founded by comedian Beppe Grillo, which wants a referendum on Italy's euro membership.
"Oh Beppe, what a fine present we are offering you by only talking about ourselves," Renzi said.
If the dissidents do form a new party, polls say they could win more than 5 percent of the vote. With the next election likely to be held under a proportional representation system, such a result could give them more power in the next parliament than if they remain in a Renzi-controlled PD.
Standing in the street outside the party meeting, a few PD supporters came to urge their leaders to stick together.
"It is vital that we remain united," said Rome architect Emma Cavallucci, holding the hand of her toddler daughter.
"Our leaders only seem to be talking to each other, not to the world outside. Don't they realize the damage they are doing us?"
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