ROME — The citizens of two northern Italian regions voted overwhelmingly on Sunday in favor of greater autonomy in closely watched referendums that come on the heels of Catalonia’s tortuous attempts to secede from Spain.

The polls closed at 11 p.m. on Sunday, and with most votes counted by early Monday, the results in Lombardy and Veneto suggested that millions of voters had cast ballots to “give a message” to the central government in Rome, Luca Zaia, president of the Veneto region, said at a news conference.

The nonbinding referendums were promoted by the Northern League, which governs both regions, and the outcome will put the regional presidents on firmer footing as they begin negotiating with Rome for greater say — and financial independence — in a number of areas, including security and immigration and education.

“This is the big bang” of institutional reforms, said Mr. Zaia in Veneto, where at least 60 percent of the population went to the polls, easily reaching the quorum of 50.1 percent. “In Veneto, what has won is the desire to be masters in our own home,” he said.