Mr. Renzi had campaigned vigorously in favor of the changes to the Constitution, but 59.1 percent of the voters rejected them.

Mr. Renzi’s government was one of only four governments to last more than 1,000 days. He came to power in 2014 after staging an internal party coup, alienating his Democratic Party’s more left-leaning factions.

The referendum and subsequent fall of Mr. Renzi further aggravated this fissure, and speculation was rife in the news media this week over Mr. Renzi’s role at the helm of the party.

“There’s an internal discussion that must be held that I think will be difficult,” Mr. Renzi told members of his party on Wednesday afternoon. But he asked that the showdown not take place until after the Italian president resolves the government crisis. Mr. Renzi also said he would not be part of the delegation that is to meet with Mr. Matterella in coming days.

The failure of the measures on the referendum call for “ample considerations,” he said during a relaxed, joke-filled 20-minute speech at the party’s headquarters. He was warmly applauded.

The problems that he, and the Parliament, had hoped to resolve through the proposed changes to the Constitution still have to be dealt with, he said.

In a nod to the populist pull of the Five Star Movement, the party set to pose the biggest threat in the next elections, Mr. Renzi took a page from their playbook and said that his party’s discussions in coming days would be streamed online. “We want to be transparent to all citizens, and to our people,” Mr. Renzi said.