"The road tragedy statistics are still horrific.... None of us are without blame and we have to start with ourselves," Medvedev said in a video blog posted on the government website.
The video -- viewable at blog.da-medvedev.ru -- begins with Medvedev sweeping around the driveway of his residence at the wheel of a black jeep, conspicuously wearing a safety belt.
He said the government would put forward legislation that would introduce a minimum punishment of five years in jail and a maximum of 15 years for causing death while drunk at the wheel.
Drunk drivers who are found speeding or jumping red lights will face massive fines of 500,000 rubles ($16,000, 12,000 euros) in Moscow and Saint Petersburg and 250,000 rubles in other regions.
Medvedev's video blog -- his favoured form of floating new ideas -- appears to be a response to a string of highly publicised accidents that have made the public more aware of road safety problems in Russia.
Prominent Russian actress Marina Golub was killed in a traffic accident in October while travelling in a taxi hit by a speeding car.
And in one particularly horrific incident in Moscow in September, a drunk driver rammed a bus stop at high speed and killed seven people including five orphans from a children's home.