Once the upper chamber of Russia's parliament, the Federation Council, approves the accession package, it then heads to the desk of President Vladimir Putin for his signature, which is expected before the July 23 deadline.
When complete, Russia will gain membership in 30 days and Congress will need to act. That means lawmakers must clear a bill that will give U.S. exporters greater access to the world's ninth largest economy, and biggest outside of the WTO, before the August recess.
"Russia’s membership in the rules-based global trading system of the WTO will contribute to Russia’s economic growth as well as provide us with new opportunities to guide and grow our bilateral economic relationship," Kirk said.
That ramps up pressure on lawmakers in Washington to clear out the Jackson-Vanik provision, which would allow for normal trade relations.
The Senate Finance Committee is planning to mark up legislation, most likely next week, that would combine a repeal of Jackson-Vanik with human-rights legislation known at the Magnitsky bill.
The House Ways and Means Committee has not announced a markup yet, and an aide told The Hill they are still working with the Obama administration and the Senate on how to move forward.
Panel Chairman Dave Camp (R-Mich.) has said he wants to move a clean repeal without any human-rights language.