"Clearly we think it's completely inappropriate and we've told them they should not do it," US State Department spokeswoman Marie Harf told reporters in Washington on Tuesday. "We don't think anyone should be providing arms to Russia."
She added that Washington had voiced its concern over the deal in recent days to French Foreign Minister Laurent Fabius.
France's contract of 1.1 billion euros ($1.5 billion) with Russia for the warships covers the construction of two helicopter carriers by the French state-owned military contractor DCNS and the French shipbuilding company STX. Each ship can carry 700 soldiers, 16 helicopter gunships, and about 50 armored vehicles.
EU foreign ministers agreed to ratchet up sanctions against Russia on Tuesday following the downing of a Malaysian airliner in Ukraine’s conflict zone.
The crash has been blamed by the US on a Russian missile system which it says was given to Ukrainian pro-Moscow activists.
France earlier said it would go ahead with delivery of the first warship, the Vladivostok, which is nearly finished, despite British-led calls for an arms embargo against Moscow. This has underlined how Europe's business ties are hindering its ability to act against Moscow over the crisis in Ukraine.
The United States and Russia are at loggerheads over Crimea, with Washington accusing Moscow of orchestrating an “illegitimate referendum to annex Crimea" and fuelling unrest in eastern Ukraine.
US officials, speaking on the condition of anonymity, told The Associated Press last week that the White House is considering imposing unilateral sanctions on Russia over the crisis in Ukraine.
Since the beginning of the crisis in Ukraine last year, the US and the EU have imposed sanctions on several Russian officials for what they perceive as Moscow’s refusal to ease tensions in Ukraine.