Luca Zaia, another League leader and the president of the Veneto region, which includes Venice and other cities marked for lockdown, said that the government had notified him about the potential ban only “at the last minute.” Since the region was kept out of discussions to draft the order, he said, “it’s literally impossible” for the region to enact it so quickly.

The government order also locks down provinces in the Emilia Romagna region south of Lombardy. Stefano Bonaccini, the region’s liberal president, implored Mr. Conte and the country’s health minister, both nominal allies, for more time to come up with a more “coherent and shared” solution.

Mayors in some of the cities marked for quarantine expressed deep ire over first hearing about the proposed order on television.

“It’s incredible,” said Rasero Maurizio, the mayor of Asti in the northern region of Piedmont, who posted a video of himself livid in a white T-shirt from his home saying that he had just heard about the potential closing of his town on television. “No one told me.”

In addition to Asti, other towns and provinces including Modena, Parma, Piacenza, Reggio Emilia, Rimini, Pesaro and Urbino, Venice, Padua, Treviso and Alessandria — all in the north — were set to be locked down.

But there were clear signs that the virus was spreading southward.

Earlier on Saturday, it touched the top of Italian politics as the leader of the governing coalition’s Democratic Party said he was infected with the virus.

“Well, it’s arrived,” Nicola Zingaretti, the leader of the Democratic Party and the president of the region of Lazio, said in a Facebook video posted Saturday. “I also have the coronavirus.”