■ Prime Minister Matteo Renzi offered his resignation on Monday, as promised. But Italy’s president, Sergio Mattarella, said in a statement that he had asked Mr. Renzi to delay stepping down until Parliament passes a budget for 2017.

■ Mr. Renzi had said he would resign after voters rejected changes to the Constitution that he supported in what amounted to a referendum on the prime minister’s government.

■ The decision to hold a referendum is another example of why political scientists say such votes are often “messy and dangerous.”

■ The results represented another victory for anti-establishment movements in Europe. “Times have changed,” said Beppe Grillo, the leader of the populist Five Star Movement.