Speaking at the same news conference in Rome on Friday, José Manuel Barroso, the departing president of the European Commission, the executive arm of the European Union, said Mr. Renzi was correct to identify the need to ease austerity policies. But Mr. Barroso suggested that the commission had already shown a sufficient degree of flexibility toward countries like France under the current rule book, and he warned that it would be hazardous to go further.

“The worst thing we could now do is to appear that we don’t respect our own rules,” Mr. Barroso said. The danger is that “the markets will start again betting against some of our member states,” said Mr. Barroso, who noted there were serious of “threats against Italy” during the recent European debt crisis.

Italian officials say their goal is to buy more time for nations using the euro to meet budget targets when they make painful structural changes in areas like pensions, workers’ rights and health care. That, however, could raise thorny issues for the European Commission, which would have to decide when such changes have been completed and whether they are sufficient to merit leniency.

Italy is putting the focus on growth at a time when its economy remains in a precarious state. Analysts say countries including Spain have done far more than Italy to make their economies more internationally competitive in the wake of the European debt crisis.

A closely watched purchasing managers’ index for Italy fell to a three-month low in June, according to a report released on Tuesday by Markit, a financial information company. Italian unemployment rose to 12.6 percent in May, compared with 12.1 percent a year earlier, according to Eurostat, the European Union’s statistics agency.