Medvedev urged Russians to be more careful and suggested stiff hikes in fines as an incentive.
"The plan is to strengthen the administrative responsibility of drivers for speeding, running red lights, crossing into the opposing lane, and other dangerous traffic violations," Medvedev said in a video posted on his Internet blog.
Medvedev's proposal included charging violators in major cities such as Moscow and St. Petersburg as much as 500,000 rubles ($16,000), Russia's RIA Novosti news agency said.
Russian lawmakers have been increasingly vocal in calling for crackdowns on drunken driving, RIA Novosti said.
The focus on bad driving sharpened this fall when a suspected drunken driver plowed into a Moscow bus stop, killing seven people.
"Even sidewalks have become unsafe," Medvedev said in an apparent reference to the September crash, RIA Novosti said.
Puzzle-maker slips 'Murdoch Is Evil' into Rupert Murdoch's Sunday Telegraph
Campus cop fatally shoots Texas student during traffic stop