The incident occured as about 100 people, among them World War II veterans, gathered for a ceremony at the Hill of Glory memorial in Lviv jointly with members of the Russian Unity and Motherland parties, the Kyiv Post reported.
When a Banner of Victory symbolising victory over fascism was being handed over, ten nationalists broke the police barricade and ran to the scene of the ceremony. Police interfered, trying to keep them in their place.
Some activists of the Svoboda (Liberty) nationalist organisation fiercely resisted police, shaking the fence put up around the Hill of Glory memorial. Scuffles erupted with police.
Ukrainian nationalists say Ukraine suffered in an identical manner from both Hitler's Germany and Stalin's USSR. But many Ukrainians, especially in the country's Russian-speaking east, have a completely different reading of history and take pride in the assertion that the former USSR contributed most to defeating fascism (see 'Background').
A victory parade was held in Ukrainian capital Kyiv on Monday, RIA Novosti reported.
Ukrainian President Viktor Yanukovych, who spoke at a rally in downtown Kyiv, said: "The victory over fascism is our festival that unites the Ukrainian people."
He warned nationalists against attempts to sow discord in society. "For the sake of cheap popularity, some activists are again trying to split Ukrainians," he said, adding that the government would "properly respond" to such actions.
But in a separate incident, a wreath which the Russian Consul-General in Lviv, Oleg Astakhov, was to lay at Lviv's military cemetery was snatched and stamped to pieces.
"Russia and the whole of the sane world are celebrating Victory Day. All of these games on this day are an insult to the memory of those buried here, who sacrificed their lives to allow us to live in a normal society," Kyiv Post quotes the Russian diplomat as saying.