The bill gives Russia and Moldova PNTR status, a necessary step if the U.S. is going to benefit form the trade concessions Russia made when it joined the World Trade Organization over the summer. But it also includes language related to human rights in Russia, a step that Democrats welcomed during debate on the rule.

Specifically, it calls for the denial of U.S. visas to Russian officials involved in the 2009 death of Russian tax lawyer Sergei Magnitsky, as well as the freezing of any U.S. assets of those officials.

Trade has been a divisive issue in Congress for more than a decade, as Democrats have argued that trade agreements need to include human-rights and environmental provisions. But Democrats said Thursday that the inclusion of the Magnitsky language makes it easy to support the bill, since it is now much more than just a regular trade bill.

"If that were all there was to H.R. 6156, it would pass or fail along familiar lines of trade-related legislation," said Rep. James McGovern (D-Mass.). "But … H.R. 6156 will become known as a landmark piece of legislation not because it grants PNTR for Russia and Moldova, but because it includes Title IV, the Sergei Magnitsky Rule of Law Accountability Act of 2012."

Rep. Sandy Levin (D-Mich.), the ranking member of the House Ways and Means Committee, added that Democrats can vote for the bill "with good conscience" because of the Magnitsky language.

Rules Committee Chairman David Dreier (R-Calif.), who is leaving at the end of the 112th Congress, said he is glad he can leave on the high note of passing a bill that has such broad support.

"It's great that we'll be able to do something with Democrats in the House, Republicans in the House, Democrats in the Senate, Republicans in the Senate and the president of the United States on the same page in support of Russia's accession to the WTO," he said.

Dreier added that House passage of the bill on Friday will fall on the anniversary of Magnitsky's death, and reiterated that passage of the bill is not to reward Russia, but to force Russia to be more accountable both economically and in the area of human rights.

"Tomorrow marks the three-year anniversary of Sergei Magnitsky's death, and it is outrageous, it is outrageous … that this kind of action in this 21st century still exists in a country that claims to be a democracy," Dreier said. "It is horrendous and it is unacceptable."