NATO Deputy Secretary-General Alexander Vershbow made the comment in a speech to a conference in Riga, Latvia.
Since last summer, reports have been circulating inside the country that many serving Russian troops have died in combat in eastern Ukraine, where more than 6,000 people have been killed in a pro-Russian insurgency.
Moscow denies sending arms or troops to the region, saying any Russians fighting in Ukraine are volunteers.
Vershbow also said "an angry, revisionist Russia that breaks international rules” and continues to destabilize Ukraine and intimidate its neighbors is one of the "new threats and challenges" faced by the Western military alliance and the European Union.
Vershbow's speech came a day after U.S. Assistant Secretary of State for European and Eurasian Affairs Victoria Nuland told a U.S. Congressional committee that Russia has sent "thousands and thousands" of soldiers and hundreds of pieces of military equipment into eastern Ukraine.
The commander of U.S. Army Europe, Lt. Gen. Ben Hodges, said this week some 12,000 Russian troops are supporting the separatists in eastern Ukraine.
Russian officials rejected those estimates Thursday.
Foreign Ministry spokesman Alexander Lukashevich said the figures were "plucked out of the air" by the United States and could "discourage and disorient the international community."
Deputy Defense Minister Anatoly Antonov responded directly to the charge that Russia has 12,000 troops in eastern Ukraine, saying: "But why 12,000? Why not 20,000, 25,000? Why are they thinking small?"
In his speech Thursday, Vershbow also said Russian President Vladimir Putin's goal "seems to be to turn Ukraine into a failed state and to suppress and discredit alternative voices in Russia so as to prevent a Russian Maidan," referring to the Ukrainian protest movement that forced Viktor Yanukovych, who was the country's pro-Moscow president, from power.
The NATO deputy secretary-general said NATO and the European Union need to increase cooperation in supporting "partners like Ukraine, Georgia, and Moldova," among others.
He also said the two organizations should coordinate their approaches to "dispel propaganda and misinformation" and defend shared democratic values.
In addition, Vershbow suggested the Russian President ultimately was responsible for the murder of Kremlin critic Boris Nemtsov.
"We've seen that the victims are not just in eastern Ukraine, with the brutal murder of Boris Nemtsov last Friday," Vershbow told members of parliament from EU countries.
Putin said on Wednesday that the killing of Nemtsov, a former deputy prime minister who was shot dead last week, was a shameful tragedy.
The Kremlin denies any involvement, saying that the killing was a "provocation" to discredit Putin.
"While we don't know who pulled the trigger, we do know that Boris Nemtsov was a powerful voice for democracy and against Russia's involvement in Ukraine ... [and] was among those vilified as "traitors" and "fifth columnists" in Russia's official propaganda," said Vershbow.
Source: Voice of America