The outspoken leader, who has clashed with EU officials over budget rules and other issues, made the comment in an interview published the day after Rome launched a push for the EU to adopt a two-speed approach to its future development.
"The EU is like the orchestra playing on the Titanic," Renzi told Bloomberg, insisting his revitalized and reformed Italy had earned the right to play a leading role in shaping the bloc's destiny.
"Today we have done reforms and we are in a position to say to EU partners: 'friends, we can change this wrong, bureaucratic approach.'"
Renzi has notably clashed with Brussels over Rome's demands for leeway on the EU's Stability Pact budget rules to allow him to revive the struggling Italian economy with tax cuts and growth-orientated spending.
Behind the technical debate over whether costs for one-off structural reforms or dealing with the migration crisis can be discounted from the calculation of deficit levels, lies a fundamental difference of economic philosophy.
Renzi has often referred to the German-inspired Stability Pact as the "Stupidity Pact".
The 41-year-old former mayor of Florence insists he is a Europhile but he often sounds like a Eurosceptic as he rails against Brussels "technocrats" or the failure of the EU to act decisively over the migrant crisis or the chaos in Libya.
He has challenged France over temporary border closures linked to migrant flows, Germany over a major gas pipeline project and fought the European Commission over the consolidation of bad debts by Italy's banks as well as budget issues.
In a reflection of Italy's more active diplomacy, Foreign Minister Paolo Gentiloni on Tuesday hosted a dinner for his counterparts from the bloc's six founding member states.
Billed as the start of a reflection on the EU's future, the ministers endorsed a statement reiterating their commitment to "ever closer union" while signalling that not all member states would be expected to pursue the goal.
Britain has demanded an opt out from the "ever closer" principle written into EU treaties as part of a package of reforms it wants agreed before holding an in-out referendum on its membership.
Prime Minister David Cameron is hoping to tie down a deal at an EU summit in Brussels on February 18th-19th.
Italy has backed Britain's right to opt out of any further pooling of sovereignty. That stance was reflected in a clause in Tuesday's Italian-drafted statement which said the EU "allows for different paths of integration."