The final vote on Thursday was expected to show overwhelming support for legislation that also imposes sanctions on Russian human rights violators.
The legislation was welcomed by American businesses concerned about falling behind in the race to win shares of the Russian market but drew rebukes from Russian officials over the human rights part of the bill.
Senate approval of legislation to establish permanent, normal trade relations with Russia would send the measure to President Barack Obama for his signature.
The House passed the legislation last month on a 365-43 vote.
Russia on Aug. 22 formally entered the World Trade Organization, requiring it to lower its import tariffs, better protect intellectual property and provide greater foreign access to its service industry. But unless Congress gets rid of existing trade restrictions and makes normal trade relations permanent, U.S. companies cannot enjoy the new trade rules available to the WTO's other 155 members.
There's already concern among U.S. companies that they will fall further behind Chinese and European competitors in gaining shares of Russia's growing market of 140 million consumers. On the other hand, the Obama administration predicts that U.S. exports of goods and services, currently at $11 billion, could double in five years if trade relations are normalized.
"We urge our colleagues to seize this opportunity that Russia's succession to the World Trade Organization presents for both job creation and our ability to bind Russia to a rule-based system of trade and dispute resolution," said Sen. John Kerry, D-Mass., chairman of the Foreign Relations Committee.
The last apparent hurdle to Senate action on the measure came with a decision to accept the House version of human rights legislation that was attached to the trade bill.
Partly in response to lawmakers critical of normalizing trade with Russia at a time when the Moscow government has taken hostile positions toward the United States and pursued anti-democratic policies at home, a provision was attached that would sanction those involved in human rights violations.
Normalizing trade, said Sen. Roger Wicker, R-Miss. "is a big win for Americans. If Congress does not act, American workers, including millions employed by small businesses, stand to lose out to foreign competitors." But normal trade alone, he said, "will not suffice when dealing with a country that continues to protect corrupt officials."
The House barred Russian human rights violators from receiving visas and froze their U.S.-based financial assets. In the Senate version, the measure applied to human rights violators around the world.
The logjam was broken when Ben Cardin, D-Md., who authored the Senate version, said he would accept the House approach so that the bill can be passed. "This bill may only apply to Russia, but it sets a standard that should be applied globally," Cardin said in a statement. "I encourage other nations to follow our lead."
Russian Prime Minister Dmitry Medvedev last week said that while his government welcomed the normalizing of trade, "we absolutely dislike its link with another legislation." He said Congress, in attaching the human rights provision, was "making a big mistake" and that Russia would respond.
The human rights provision is named for Sergei Magnitsky, a Russian lawyer and whistle-blower who died in a Russian prison three years ago after allegedly being tortured.
The Moscow government has voiced strong opposition to the Magnitsky language, saying it would increase tensions between the two countries and hinting at retaliation.
The trade bill eliminates the Jackson-Vanik amendment to a 1974 trade bill that tied trade with the Soviet Union to greater freedom for Jews and other Soviet minorities to emigrate.
Although the amendment has long outlived its purpose and is now annually waived by presidents, it has never been removed from the books, preventing the establishment of permanent normal trade relations.