The draft resolution asserts that US President Donald Trump is trying to normalize relations with Russia, instead of using all available tools to combat "Russian threats."
"Today's resolution makes it clear that the US Senate will be against re-admitting Russia until it stops its harmful actions against Ukraine, our allies and the United States," RIA Novosti quoted the project as saying.
Earlier, Trump said that Washington insisted on excluding Russia from the G8, since Moscow outplayed ex-US President Barack Obama in foreign policy.
US Secretary of State Mike Pompeo said that it is necessary to interact with the Russian side more often, but Trump should take the decision to invite Russia to the G7.