CHARLESTON, W.Va. — West Virginia’s Republican-controlled Senate on Tuesday passed another tax bill backed by Democratic Gov. Jim Justice that would cut all state income tax rates while raising the sales tax.

The latest bill is similar to two previous measures rejected by the Republican-controlled House, though it contains some modifications intended to soften opposition.

It would raise the sales tax from 6 percent to 6.85 percent, fractionally less than the previous proposal. It would lower the top tax rate from 6.5 percent to 6 percent, cut the lowest rate from 3 percent to 2.25 percent and reduce those in between. It contains a provision to eventually end all those taxes depending on increases in other state revenues.

The Senate voted 19-11 for the bill after rejecting an alternative backed by Democrats that would have exempted Social Security payments from state income taxes instead of cutting all income tax rates.

“There are about 312,000 people in the state that receive Social Security benefits,” said Sen. Roman Prezioso, the chamber’s minority leader. “There’s a tremendous amount of money that West Virginia receives from the federal government, about $6.2 billion in Social Security benefits. And just think, giving that money back to our most vulnerable citizens, the people that need the help, those folks will go out and spend the money and get a greater return on every dollar that’s spent.”

Sen. Mike Romano, a Clarksburg Democrat, backed the Social Security tax break, saying it would give the state economy a boost with more spending. The other bill would give people making more money, like himself, a tax break they don’t need, and “the trickle down theory” that such breaks benefit the overall economy has been shown not to work, he said.

Sen. Robert Karnes, a Republican who chairs a tax committee that first proposed ending income taxes, said advocates for seniors told them that low-income elderly already pay little or no income tax on Social Security benefits.

Sen. Charles Trump, a Morgan County Republican, said the broad rate cuts mean income-tax relief for everybody. “Every West Virginians, including those seniors, will get relief,” he said.

Justice appeared in the Senate Tuesday afternoon before the vote, urging adoption of his budget plan including the tax overhaul that would close a projected budget deficit.

The House adjourned until Wednesday, without discussing the tax bill, having sent it to the Finance Committee.