"I congratulate you from my very heart with the day of the great victory, with a celebration which always was and will remain the most national and sacred and which has become for ever a symbol of our national unity," he said.
Medvedev also criticised "intentions to intrude in the affairs of other states and especially redraw borders" In an apparent attack on US foreign policy and Western backing for the independence of Kosovo.
The May parade comemorates the 27 million Soviets who were killed in World War II, known in Russia, which has nearly quadrupled its defence spending in recent years, as the Great Patriotic War.
Jonah Hull, Al Jazeera's correspondent in Moscow, said: "This [parade] caps a political change in Russia, with a new president and a new prime minister … and is a message as much to the world as to the Russian people, that as well as political stability Russia also has military clout."
Vladimir Putin, the former president who was confirmed in the prime minister's post on Thursday and retains major influence, stood alongside Medvedev for the parade.
Putin earlier said the parade was not "sabre-rattling" but "a demonstration of our growing defence capability."
In recent days tensions between Russia and its US-backed neighbour Georgia have reached new heights amid differences over the Moscow-backed separatist territory of Abkhazia.