The Russian military says more than 2,000 servicemen are taking part in "large-scale" air-defense exercises in southern Russia, Crimea, and the breakaway Georgian regions of Abkhazia and South Ossetia.

The military's Southern Federal District said on March 5 that 500 pieces of heavy weaponry or military equipment were being used in the drills conducted by air-defense units, whose job is to repel attacks by aircraft and missiles.

In a statement, it said drills were taking place at 12 training grounds in Russia's Southern, North Caucasus, and Crimean federal districts, as well as at bases in Abkhazia and South Ossetia.

It was not immediately clear how long they would last.

Previous exercises in western and southern Russia have raised concerns among neighbors and prompted accusations that Moscow has used them as cover for sending forces into Ukraine to support rebels in a conflict that has killed more than 6,000 people since April.

Russia annexed Crimea from Ukraine in March 2014 and recognized Abkhazia and South Ossetia as independent countries in 2008 -- both moves that have been widely condemned by other nations.

At an unrelated news conference in Moscow, Deputy Defense Minister Anatoly Antonov claimed that NATO is more active near Russia's borders than Russia itself.

Antonov accused the Western alliance of using the conflict in Ukraine "as a pretext" to "move on, closer to Russia's borders."

"NATO activity is much higher than that of the Russian armed forces," he said.

At the same time, Antonov said NATO activity "is not posing any serious threat to the security of the Russian Federation."

"The Russian armed forces are acting appropriately and remain prepared for any turn of events," he said.

The conflict in Ukraine has caused the most severe tension in relations between Russia and the West since the Cold War.

But Antonov suggested any Western concerns that Russia could launch an offensive further west into Europe were unfounded.

Antonov said that at a security conference in Munich last month, speakers "made some crazy, paranoid allegations as if we were planning to launch an offensive with our tank armadas, planes, and ships. I was looking at those people and thinking, 'Are you out of your minds?'"

Russia denies it has sent troops and weapons into Ukraine to support the separatists, despite what NATO says is incontrovertible evidence it has done so.

U.S. Army Europe Commander Ben Hodges said on March 3 that the U.S. military estimates some 12,000 Russian soldiers -- including military advisers, weapons operators, and combat troops -- are supporting the separatists.

Meanwhile, Russian Foreign Ministry spokesman Aleksandr Lukashevich claimed on March 5 that "according to information we possess" some 300 U.S. servicemen from the 173rd Airborne Brigade based in Italy were due to arrive in the western Ukrainian city of Lviv to train Ukrainian soldiers "how to operate military hardware from across the ocean."

Lukashevich also called the presence of NATO warships in the Black Sea an "alarming signal and a provocative idea."

NATO warships have regularly entered the Black Sea for many years but their presence there since the conflict erupted in Ukraine has been subject of extra attention in Russia.

With reporting by RIA, Interfax, TASS, and Reuters