No Most Favored Nation Trading with Russia Act This bill withdraws normal trade relations treatment from Russia. Additionally, the bill requires the President to encourage U.S. allies and partners to (1) consider taking similar actions; and (2) condemn, at the World Trade Organization (WTO), Russia's aggression in Ukraine. Further, the President must direct the U.S. Permanent Representative to the WTO to seek suspension of Russia's membership in the WTO. The President may proclaim modifications to the applicable duty rates on products from Russia (under column 2 of the Harmonized Tariff Schedule) if the President determines that the modifications are necessary to protect the essential security of the United States.