The United States is preparing fresh sanctions against Russia over the near-fatal poisoning of Kremlin critic Alexei Navalny, a top White House advisor warned Sunday.

Jailed opposition leader Navalny, President Vladimir Putin's most prominent opponent, was arrested in January upon returning to Russia after recovering from a poisoning he says was orchestrated by Moscow.

"We have sanctioned Russia for the poisoning of Alexei Navalny... We rallied European allies in a joint effort to impose costs on Russia for the use of a chemical agent against one of their citizens on Russian soil," US President Joe Biden's national security advisor Jake Sullivan told CNN's "State of the Union."

The United States in March imposed sanctions on the director of Russia's FSB security agency after finding it carried out the poisoning of Navalny.

"We are preparing another package of sanctions to apply in this case, as well. We've shown along the way we're not going to pull our punches," Sullivan added.

He spoke days after Biden and Putin met in Geneva for their first summit, where the leaders sought to cool tensions in the combustible US-Russian relationship.

Diplomatic relations between Moscow and Washington had all but broken down since Biden took office in January.

After Biden likened Putin to a "killer," Russia in March took the rare step of recalling its ambassador Anatoly Antonov. The US envoy, John Sullivan, likewise returned to Washington.

Putin rejected criticism of his treatment of opponents -- many high-profile critics have been killed in Russia during his rule and the media is almost entirely muzzled -- saying that the United States had bigger problems.

A day after the summit, the Kremlin was guarded about future dialogue with Washington.

"We are ready to continue this dialogue to the same extent as the American side is," Putin said in televised remarks.

The Russian leader said the meeting was "quite friendly" and that he and Biden "were able to understand each other on key issues."