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.