ALBANY — The state shouldn’t simply renew the so-called millionaire’s tax but perhaps even raise rates for those earning $5 million, $10 million or more annually, the top Democrat in the State Legislature said Wednesday.

Assembly Speaker Carl Heastie (D-Bronx) said New York should consider raising income-tax rates even higher for big earners. His position sets up one of the biggest fights over the 2017-18 state budget, as Gov. Andrew M. Cuomo wants to simply renew the tax and the Republican-led Senate wants to kill it.

“We still want to go beyond that,” Heastie, referring to Cuomo’s proposal, told reporters outside the Assembly chambers. “Just the extension of the millionaire’s tax won’t satisfy the [Assembly Democrats’] needs to provide more education. . . . We believe we want to add a couple more tiers for the highest-earning millionaires in the state.”

A day earlier, Cuomo made public his $162 billion spending proposal that would boost aid to elementary and secondary schools by 4 percent ($1 billion), $2 billion for water infrastructure, provide $260 million to help nonprofit social services agencies adapt to the state’s rising minimum wage, and spend $163 million to create a pathway to free college tuition at public universities.

Cuomo unveiled his proposal in an unusual fashion, providing private briefings to some blocs of legislators, skipping others because the daily legislative session ran long Tuesday and not formally making the entire plan available online until after 8:30 p.m.

As such, New York’s 213 state legislators were just beginning to pore over the document Wednesday to determine Cuomo’s proposal for individual school districts and key programs.

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“What they presented and what we actually find, hopefully they’re the same thing,” said Senate Majority Leader John Flanagan (R-East Northport). For instance, he added: “If there is a billion-dollar increase in education, but it’s not equitably distributed, that’s a problem.”

The millionaire’s tax, first imposed in 2009 amid the Great Recession, is a key cog in the plan. Cuomo opposed the tax in 2011, his first year in office, but changed his mind and has since gotten the legislature to renew it twice. It is set to expire Dec. 31.

The tax, imposed on individuals who earn $1 million or more annually and couples earning $2 million, brings in more than $2 billion a year to state coffers. With the state already facing a $3 billion revenue shortfall this year, Cuomo said he can’t allow the millionaire’s tax to expire.

Heastie said Cuomo’s budget plan doesn’t have “enough money for education” if Assembly Democrats and the governor want to meet their 2017 goals. The speaker said imposing a higher rate for some might be doable because there might be “some federal action that’s going to benefit the millionaires in this state” — referring to President-elect Donald Trump’s vow to cut income taxes.