"The victory won in 1945 was our common victory, a victory of good over evil, of justice over lawlessness," Russian President Dmitry Medvedev said at a reception honoring veterans after the parade.
Including military representatives from other countries in Sunday's parade, Medvedev said, "is indicative of our solidarity, and of the understanding that universal humanistic values are becoming increasingly important for the development of the modern world."
Chinese President Hu Jintao and German Chancellor Angela Merkel were among the parade's invited guests.
Millions of Russians watched the parade on television and attended smaller parades in cities across the country, and more than half of Russians greeted the invitation to foreign troops with approval, according to a poll by the independent Levada Center in April.
But leaders of the Communist Party and right-wing organizations have criticized the change. And in a country that still regards the U.S.-led NATO alliance as its primary security threat, 20 percent of respondents to Levada's poll said they disapproved of inviting international troops to march in the parade, and 8 percent were strongly against it.
The Soviet Union suffered the most losses of any country during World War II, with more than 7.5 million soldiers killed and 5 million wounded, along with millions of civilian deaths.
Most Russians say they believe the Red Army would have defeated Hitler without Western assistance, Levada's research shows.