It's the pre-USSR Russian Empire that Putin wants to reclaim, not "recreate the USSR". It's a very important distinction.
The USSR was dominated by Russia but the Soviets were the ones that set up the republics that surrounded it like Ukraine, Kazakhstan, etc. The ealy Bolsheviks were largely an alliance of separatist ethnic nationalist movements in those regions and an urban working class revolutionary movement (or "vanguard", I guess more accurately). The Tsars spent centuries trying to wipe out rebels in places like Ukraine, but the Soviets did the complete opposite - they gave them their own republics within the wider Soviet Union, legally an equal with Russia (even if in practice, as I say, it was Russia-dominated).
Putin was very explicit in his speech earlier this week that he blames Lenin for giving people like the Ukrainians what he considers to be an illegitimate right to independence. He wants to redraw the map of Eurasia, back to 1917, when they knew their place. It's also central to the whole "NATO is expanding into 'our' part of Europe" issue - clearly Russia is the aggressor here, but as far as the Russian nationalists in the Kremlin are concerned NATO has got in and claimed those countries before Russia could reabsorb them.
