That could leave it open for the Senate to drop in its bill, which it combined with the PNTR bill, which is identical to the House version, in the Senate Finance Committee in July.
House Ways and Means ranking member Sandy Levin (D-Mich.) said during the hearing that he would like to work on expanding the breadth of the human rights language.
The House measure also includes additional enforcement provisions, requires the Obama administration to report on Russia's implementation of WTO rules and gather information on bribery and corruption.
The Obama administration announced Tuesday evening that is strongly supports the measure, which also normalizes trade relations with Moldova.
"For American businesses, workers, farmers and ranchers to reap the same economic benefits in Russia's markets that other WTO members receive, the Congress must end" Jackson-Vanik, an obsolete U.S. law aimed at encouraging the emigration of Russian Jews with the threat of higher tariffs.
"The administration seeks to promote the rule of law and respect for human rights around the world and intends to continue working with the Congress to support those seeking a free and democratic future for Russia."