"Our army and navy are gaining strength", he said.
"And in their power today lies the historical glory of Russian arms, therein lies the traditions of victory and the high spirit of our army."
His predecessor, Vladimir Putin, said earlier that the display of heavy weapons in this year's Victory Day parade was "not sabre-rattling", but "a demonstration of our growing defence capability".
Show of military might
Marching bands and 8,000 troops goose-stepped across Red Square, and heavy weapons such as Topol-M ballistic missiles and T-90 tanks were on display.
The cobbles of Red Square had been reinforced, in advance of the parade, to cope with the tanks and other heavy weaponry.
Television stations showed soldiers marching in cities around the country, as well as veterans with chests laden with medals.
Russia has made other recent shows of its military capability, including the resumption of long-range flights by the Tupolev Tu-95 bomber, an icon of the old Soviet arsenal.
But analysts say that despite these signs of military might, there is evidence of the Russian army and navy suffering from lack of money, a shortage of training, and low morale.
The BBC's Rupert Wingfield-Hayes in Moscow says conscripts in the army can be subjected to shocking brutality.
Last year 450 conscripts died from beatings or suicide.
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