WASHINGTON — The Senate voted on Thursday to finally eliminate cold war-era trade restrictions on Russia, but at the same time it condemned Moscow for human rights abuses, threatening to further strain an already delicate relationship with the Kremlin.

The Senate bill, which passed the House last month, now goes to President Obama, who has opposed using United States trade policy to make a statement about the Russian government’s treatment of its people.

But with such overwhelming support in Congress — the measure passed the Senate 92 to 4 and the House 365 to 43 — the White House has had little leverage to press its case.

And President Obama has shown little desire to pick a fight in which he would appear to be siding with the Russians on such an issue.

In a statement issued after the Senate vote, the White House mentioned the human rights component of the bill only in passing, instead emphasizing that the president was looking forward to signing a measure that would level the playing field for American workers.

The most immediate effect of the bill would be to formally normalize trade relations with Russia after nearly 40 years. Since the 1970s, commerce between Russia and the United States has been subject to restrictions that were intended to punish Communist nations that kept their citizens from emigrating freely.

While presidents have waived the restrictions since the cold war ended — allowing them to remain on the books as a symbolic sore point with the Russians — the issue took on new urgency this summer after Russia joined the World Trade Organization. As part of its pact with the trade group, Russia lowered tariffs for other member countries, but only those that granted it normal trade status.

By some estimates, American exports to Russia are expected to double after its trade status is revised.

But another effect of the bill — and one that has Russian officials furious with Washington — will be to require that the federal government freeze the assets of Russians implicated in human rights abuses and deny them visas.

Lawmakers on Capitol Hill were inspired to attach those provisions to the trade legislation because of the case of Sergei L. Magnitsky, a Russian lawyer who sustained serious injuries and died in a Moscow detention center in 2009 after he accused government officials of a tax fraud scheme.

During the Senate debate, it was Mr. Magnitsky’s case, and not Russia’s trade status, that occupied most of the time.

One by one, Democratic and Republican senators alike rose to denounce Russian officials for their disregard for basic freedoms.

“This culture of impunity in Russia has been growing worse and worse,” said Senator John McCain, Republican of Arizona. “There are still many people who look at the Magnitsky Act as anti-Russia. I disagree,” he added. “Ultimately passing this legislation will place the United States squarely on the side of the Russian people and the right side of Russian history, which appears to be approaching a crossroads.”

In Moscow, the denunciation was swift, and legislators promised retaliation with a proposal of their own that would freeze the bank accounts of American human rights violators.

“This initiative is intended to restrict the rights of Russian citizens, which we consider completely unjust and baseless,” said Konstantin Dolgov, the Russian foreign ministry’s human rights envoy, in comments to the Interfax news agency in Brussels. “This is an attempt to interfere in our internal affairs, in the authority of Russia’s investigative and judicial organs, which continue to investigate the Magnitsky case.”

Russian officials have said that Mr. Magnitsky is not the hero his supporters make him out to be, and they have pursued posthumous tax evasion charges against him. And lately the case has taken some more unusual turns. One witness was recently found dead in Britain.

Initially the Senate faced some pressure to pass a bill that punished human rights violators from all nations, not just those who are Russian. But the House bill applied only to Russia. And the Senate followed suit, as supporters of the bill wanted something that would pass quickly and not require a complicated back-and-forth with the House.

But Senator Ben Cardin, a Democrat from Maryland who wrote the bill that would apply internationally to all nations, said the United States position on human rights abusers was unambiguous. “This bill is our standard,” he said. “The world is on notice.”