Clinton said following a meeting with human rights leaders in Ireland this week that Russian efforts to create a Eurasian trade block was tantamount to a move to "re-Sovietize" Eastern Europe and Central Asia.
The European government recently launched an anti-trust investigation into Russian energy contracts in the region. Russia's state-run news agency RIA Novosti described the trade union as an effort by Russian President Vladimir Putin to shore up ties with former Soviet republics.
Alexander Grushko, Russia's envoy to NATO, downplayed Clinton's remarks, saying the Kremlin wasn't backsliding.
"Sovietization is a cliche which, in my opinion, is absolutely incongruous with the actual processes that are taking place throughout the former U.S.S.R.," he was quoted by the Russian news agency as saying.
During the summer, both sides traded barbs over plans for a missile defense system in Eastern Europe. The Kremlin said it would upset the regional balance of power, though Washington said it was necessary protection against Iran and North Korea.
Moscow, meanwhile, expressed frustration after U.S. lawmakers passed the Magnitsky Act, a bill that would target Russian officials thought to be tied to the 2009 death of Kremlin critic Sergei Magnitsky.
The act is part of legislation that would grant permanent normal trade status to Russia.