The Progressive and Democratic Movement (DP) has emerged as the union of left-wing defectors from the ruling Democratic Party (PD) and part of the Sinistra Italiana (the Italian Left, I).
"We want to build an open movement... that is also the beginning of a centre-left renewal", the party said in its founding manifesto.
In a sharp jab at Renzi's leadership, the DP said it would "get back on track and abandon the tack" to the political right undertaken since he became prime minister in February 2014.
The DP said it aimed to restore a centre-left party of alliances "which will not suffocate under the ambitions of its leader and the arrogant pretension of self-sufficiency that would inevitably lead our adversaries to victory".
The party creators cited The Olive Tree, the left-wing coalition led by Romano Prodi which won legislative elections in 1996 and 2006, as a model for a multi-faceted alliance for the political left.
The left-wing rebels who had been sparring with Renzi accused him of stifling debate within the ruling Democratic Party.
The new movement is headed by the ruling party's former leader in parliament, Roberto Speranza and Enrico Rossi, the head of the Tuscany region.
Former PD boss Pier Luigi Bersani and another former prime minister, Massimo D'Alema, are also among the supporters.
"We are all here because we have an adversary - the right and its populist offshoot - and we can only beat them by building a left", Rossi said.
The new DP party is likely to throw its support behind current Prime Minister Paolo Gentiloni, pushing for him to remain in place until the scheduled end of the legislative term, in February 2018.
Renzi, meanwhile, has pushed for earlier elections and may seek a vote as early as September.
Italy's biggest opposition party, the Five Stars Movement, is also keen for early elections, as is the anti-immigrant Northern League, while the centre-right wants to wait.
Renzi, 42, is accused of failing to reboot the country's flagging economy - which has barely grown since 2000 - or tackle the jobless rate, which had hovered around 11.5 percent for over a year when he quit in December.