The decision comes after Putin said during the plenary session of the Valdai Discussion Club in October that Moscow could mirror Washington's stance and withdraw the treaty's ratification from the lower house of parliament.
Russian State Duma Speaker Vyacheslav Volodin later said the lower house would take up the issue at its next session in a mirror response to the US move.
The CTBT, adopted by the UN General Assembly in September 1996, prohibits all nuclear explosions, whether for military or peaceful purposes.
The document has not yet entered into force because eight countries have not ratified the treaty, including China, Egypt, India, Iran, Israel, North Korea, Pakistan and the United States.
Withdrawal from the CTBT is possible only in the event of emergencies threatening the supreme interests of the Member State and upon six months' notice.