"The nature of the exercises, and attempts to present them as anti-Russian, as well as the involvement of countries from outside the region cannot but provoke certain questions and certain concerns. Why was the Black Sea basin chosen for the drills?" the ministry said on its website, describing the purpose of the exercises as "questionable."
The Russian ministry said Black Sea countries can independently, without outside interference, solve Black Sea security and stability issues.
The ministry also said that the current military exercises had been met by protests from the local population, and that the demonstrations reflected Ukrainian public opinion in relation to the current Ukrainian administration's policy of seeking membership of NATO. The statement also said that this policy did nothing to improve relations with Moscow.
Sea Breeze 2008, a NATO military exercise, began on Monday in Ukraine's Odessa, Crimea and Black Sea coastal regions. Two years ago, the Sea Breeze 2006 exercise in the Crimea was disrupted by protests.
Ukraine and the United States are joined by 15 other countries for this year's exercises, which are due to end on July 26. Fifteen Ukrainian ships, four aircraft, 10 helicopters, and 500 service personnel are involved in the military exercises.
Ukraine's parliament, the Supreme Rada, approved NATO participation in the exercises in April. In total, more than 1,000 NATO troops, 15 ships, two submarines, and eight aircraft are expected to take part.
In May and June, several Ukrainian left-wing politicians announced that they would organize mass protests to disrupt the drills. Last Thursday, some 20 opposition activists set up an encampment in western Crimea, intending to picket the exercise.
A branch of the Ukrainian Communist Party in Donetsk said over 1,000 people took part in anti-NATO rallies in the Donetsk Region in eastern Ukraine.
The Ukrainian Progressive Socialist Party said on Wednesday that authorities in Ukraine's Odessa region had banned broadcasts by Russian television channels over their coverage of the Sea Breeze 2008 exercise and the accompanying protests.
Ukraine's pro-Western leadership has been pursuing NATO membership since 2004, when President Viktor Yushchenko came to power. Ukraine failed to secure a place in the NATO Membership Action Plan, a key step toward joining the alliance, at a NATO summit in April, but was told the decision would be reviewed in December.
A poll conducted in April by the FOM-Ukraina pollster indicated that a majority of Ukrainians oppose NATO membership.