The party, which opposes Ukraine's bid to join to NATO and has organized a series of anti-NATO protests throughout the country, said the authorities in Odessa had demanded cable networks stop transmission of Russian channels.
"This is the way the Ukrainian authorities and their representatives in Odessa have responded to the truthful information about the protests against Ukraine's NATO membership and the holding of the Sea Breeze 2008 exercise," the party said on its website.
The National Television and Radio Broadcasting Committee, which issues broadcasting licenses, declined to comment on the report.
Sea Breeze 2008, a NATO military exercise, began Monday in Ukraine's Odessa, Crimea and Black Sea coastal regions.
Ukraine and the United States are joined by 15 other countries for this year's exercises, which end July 26. Fifteen Ukrainian ships, four aircraft, 10 helicopters and 500 service personnel will take part in the military exercises.
Ukraine's parliament, the Supreme Rada, approved NATO participation in the exercises in April. 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 and disrupt the drills. Last Thursday, some 20 opposition activists set up an encampment in western Crimea, intending to picket the exercise.
Two years ago, the Sea Breeze 2006 exercise in the Crimea was obstructed by protests, forcing the United States to change the deployment of the Advantage cargo ship.
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 showed a majority of Ukrainians oppose NATO membership.
