"We are preparing another package of sanctions to apply in this case," Sullivan told CNN's Dana Bash on "State of the Union." "We've shown all along the way that we are not going to pull our punches, whether it's on solar winds, or election interference, or Navalny when it comes to responding to Russia's harmful activities."

Sullivan said the sanctions will come once the US can "ensure that we are getting the right targets," adding, "When we do that, we will impose further sanctions with respect to chemical weapons."

Sullivan's comments come days after President Joe Biden's three-hour summit in Geneva with Russian President Vladimir Putin that capped off his first foreign tour since taking office.

Biden and Putin each described the meeting as generally positive but without any major breakthroughs.

And Biden, who has since turned back to his agenda at home, has said proof of progress with Russia will come later, when the results of his diplomacy bear out.

Biden said last week that he warned Putin during their meeting of the consequences if Navalny were to die in prison, telling reporters: "I made it clear to him that I believe the consequences of that would be devastating for Russia."

The Biden administration imposed a raft of sanctions on Russian officials and entities in March over the poisoning and imprisonment.