Keeping Russia's Energy and Military Liable for Invading its Neighbors Act or the KREMLIN Act This bill temporarily prohibits federal agencies from contracting with persons that have business operations with the government of Russia or with fossil fuel companies that operate there, with exceptions where necessary to provide humanitarian assistance or disaster relief or where vital to U.S. national security interests. The bill terminates the prohibition when the President submits to specified congressional committees a written certification determining that Russia has reached an agreement relating to the withdrawal of Russian forces and cessation of military hostilities that is accepted by the Ukrainian government, poses no immediate military threat of aggression to any North Atlantic Treaty Organization member, and recognizes the right of the people of Ukraine to independently and freely choose their own government.