Congress on Wednesday cleared a measure to block a Labor Department rule that allows retirement plan managers to incorporate climate and social considerations into their investment decisions, setting up a veto fight with President Biden over an otherwise obscure regulation that has become a flash point in the culture wars.

The Senate passed the resolution by a vote of 50 to 46 after two Democrats, Senators Jon Tester of Montana and Joe Manchin III of West Virginia, joined every Republican. Coming the day after the House approved the measure on a mostly party-line vote, that cleared the measure to be sent to the White House, where Mr. Biden’s advisers have said he plans to veto it.

The vote was the latest piece of a broader Republican political strategy to portray Mr. Biden’s policies as extreme liberalism run amok, and to characterize his administration’s actions as attempts to force progressive values into every area of American life. The rule in question, which was updated in December, allows retirement funds to consider climate change and other factors when choosing their investments. The Biden administration put it in place to counter a rule instituted in 2020 by the Trump administration that sought to limit the ability of retirement and pension plans to consider those issues.

For nearly two decades, major corporations around the globe have widely accepted principles known as E.S.G. — short for environmental, social and governance factors. Republicans have taken aim at the philosophy, which essentially holds that companies should be focused at least in part on how their businesses affect the environment and society — not solely on profits — calling it a prime example of how Democrats and liberals have sought to impose their views on the rest of the country.

“The Biden administration wants retirement plan managers to invest people’s retirement funds based not on the best return for the money — nope — based on woke ideology,” Senator John Barrasso, Republican of Wyoming, said on Wednesday, characterizing Mr. Biden’s priorities as those of the “radical left.”

Republicans also argue that the rule would lead to disinvestment from the fossil fuel industry, jeopardizing tax revenues and jobs. Both Mr. Manchin and Mr. Tester face re-election races next year in states that rely heavily on fossil fuels.

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