New York already offers in-state students one of the lowest tuition rates in the nation. Current full-time tuition at four-year State University of New York schools for residents is $6,470; at two-year community colleges, the cost is $4,350. Full-time costs for City University of New York schools are about the same. The state also provides nearly $1 billion in support through its tuition assistance program, which has an adjusted gross income limit of just under $100,000. Those awards top out at $5,165; many grants are smaller.

Costs for the state could also rise as enrollment rises. Some 400,000 students attend state or city universities full time, but the administration projects that the lure of a tuition-free system could increase the student population by 10 percent by 2019.

Estimates for other free-tuition proposals have said that costs would be even higher. A 2015 report by the city’s Independent Budget Office put the cost for the city’s community colleges alone at $138 million to $232 million. But Mr. Malatras expressed confidence in the administration’s estimate, saying it had calculated costs considering a variety of factors, including the number of students receiving money through federal Pell grants, the state tuition assistance program and tuition credits.

But even some supporters expressed some doubt about how much Mr. Cuomo’s plan could cost the state. “The cost estimate of $163 million begs the question: If it costs so little, why haven’t we done it before?” said Assemblywoman Deborah J. Glick, the chairwoman of the Assembly’s Higher Education Committee.

The tuition plan will require legislative approval, a potential challenge when the governor and lawmakers have been at odds over a raise and other issues. On Tuesday, Democrats and Republicans offered qualified support for the plan, saying they wanted more details on the proposal and adding that each party had also worked to lower tuition.

“We are pleased to see the governor join us in our efforts,” said Michael Whyland, a spokesman for Carl Heastie, speaker of the Democrat-dominated Assembly, noting that his fellow Democrats had made similar proposals for free tuition in the past. Scott Reif, a spokesman for the Republicans, who rule the Senate with the help of a group of breakaway Democrats, said his party had “been fighting for years to expand TAP eligibility,” referring to the tuition assistance program.

“This proposal appears to move us in a positive direction,” he said.

Bruce Gyory, an Albany-based political consultant, said the governor’s announcement would appeal to the voters who flocked to Mr. Sanders during the Democratic presidential primaries last year — and to voters with some college education but no degree, who swung to Donald J. Trump in the general election. Such voters made up nearly a third of the electorate, according to exit polls, Mr. Gyory said.