The nationalists Lega Nord, led by Steve Bannon ally Matteo Salvini, were criticized by Luigi Di Maio, leader of their populist coalition partner the Five Star Movement.
Health Minister Giulia Grillo said it is time to "give space to the new."
After dozens of people were killed in the collapse, Italy's deputy prime minister seemed to point the finger at "external constraints."
Nearly three months since the vote, Italy's new prime minister—an academic with no political experience—will lead a team of the predominantly male, populist and euroskeptic.
'Only the coward runs away in times of trouble,' the ex-Prime Minister said.
Beppe Grillo's party was rejected from joining a liberal grouping.
Some 78.5 percent of members who voted backed the party's new alliance.
Renzi resigned on Wednesday after his referendum defeat.
An election in one of the EU's most Euroskeptic nations would add to fears of populist uprisings.
Insurgents' success means more worry for Europe's centrists.
Matteo Renzi's center-left government could face tough contests in four cities.
John Mills, Deputy Chair of Brexit group Vote Leave, says party is out of touch with supporters on Europe.