"Russia would be a pioneer in a new sport," said Lebedev, who also suggested fights between different fan groups could draw crowds of thousands.
"English fans arrive, for example, and start picking fights, and they get the answer - challenge accepted. A meeting in a stadium at a set time."
Reports of Lebedev's proposal were met with disbelief in England. Former international Gary Lineker tweeted: "WTF? Is he insane?", while columnist Colin Murray called the Russian politician "an absolute w***er".
Some fan groups in Russia already hold illicit fights along similar lines, typically pre-arranged mass brawls in rural locations, away from police.
A Russian Premier League game on Sunday between CSKA Moscow and Zenit St. Petersburg was marred by clashes between small groups of rival fans, who fought one another and tried to break through a security fence.
It isn't the first time Lebedev has courted controversy with his views on hooligans. He hailed the violence in Marseilles last year, telling Russian fans: "Well done lads, keep it up!"
Besides his parliamentary duties, Lebedev is also on the board of the Russian Football Union.
He's a long-time associate of fan leader Alexander Shprygin, who was deported from France last year following the Marseilles violence. Two board members of an organisation run by Shprygin were given prison sentences.
Despite his enthusiasm for soccer-related violence, Lebedev insisted Russian policing meant foreign fans wouldn't be in danger at the World Cup.
"We've taken all the safety measures, modernised legislation. Not a single tourist has any reason to fear travelling to our country in the summer of 2018."