…And the Communists want a recount.
With nearly 80% of ballots counted, his United Russia had over 63% of the vote. The opposition Communists and two other parties also look set to win seats.
Opposition allegations of fraud were dismissed by the electoral commission.
Mr Putin has said a strong result would give him the authority to retain political power after his presidential term ends next year, possibly as PM.
The Communists say they will mount a legal challenge to the result. They said a meeting would be held later on Monday to decide whether to boycott the new parliament.
“We do not trust these figures announced by the central elections commission and we will conduct a parallel count,” Communist Party leader Gennady Zyuganov said.
The White House also urged Russian authorities to investigate reports of fraud.
United Russia’s leader, Boris Gryzlov, acknowledged there had been violations but dismissed them as insignificant.
“They in no way put in doubt the final result. The fact that these violations have been registered shows that we have a transparent ballot,” he said.