Fellow lawmaker Andrei Lugovoi, who was one of the five Russians targeted in the latest extension of United States sanctions, said the measure was absurd.
Bastrykin, officials said, was complicit in the case of Sergei L Magnitsky, an anti-corruption lawyer who mysteriously died in Russian detention in 2009 and after whom the Magnitsky Act was named by the US Congress.
The pair are suspected of murdering Putin critic and ex-spy Litvinenko in London using radioactive polonium 11 years ago. Among the officials is senior federal investigator Aleksandr Bastrykin, considered a close aide to president Vladimir Putin.
The US Treasury Department announced on Monday that the sanctions were meant to punish Russian Federation over what it called human rights abuses.
Kremlin spokesman Dmitry Peskov told reporters Washington's decision to blacklist Investigative Committee chief Alexander Bastrykin and Litvinenko's alleged assassins, lawmaker Andrei Lugovoi and Dmitri Kovtun, represented "further steps in the artificially created degradation of our relations".
Kirby said the individuals had "roles in the repressive machinery of Russia's law enforcement systems, as well as individuals involved in notorious human rights violations".
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Through the related 2013 Magnitsky Act [text], the Treasury Department has led a campaign to freeze assets, prohibit all transactions and deny visas to Russians implicated in human rights abuses.
The new sanctions came less than two weeks before President-elect Donald Trump is set to succeed outgoing President Barack Obama. He added that at the moment he could not say whether Moscow would take any retaliatory measures in response to these sanctions.
Moscow has vehemently rejected the accusations, over which Washington has already expelled 35 Russian diplomats allegedly involved in espionage and due to what Obama said was "harassment" of U.S. diplomats in Russia.
The other two Russians hit with the new Treasury sanctions are banker Gennady Plaksin and law-enforcement official Stanislav Gordievsky, whom Magnitsky's supporters accuse of involvement in the massive theft and the late auditor's alleged persecution, respectively.
The Chairman of Russia's Defense and Security Committee, Victor Ozerov, told TASS news agency that the addition of Bastrykin to the "Magnitsky list" will complicate cooperation between Russian security forces and their worldwide counterparts but will fail to inflict any long-term damage.