The leftist Sergei Udaltsov is among several opposition figures charged with riots and violence against police during a protest against Mr Putin in May on the eve of the former KGB spy's inauguration for a third presidential term.
The federal Investigative Committee, which answers only to Mr Putin, has so far only barred Mr Udaltsov from travelling freely as he awaits trial.
However, yesterday, investigators said Mr Udaltsov was not complying with that and they were now seeking house arrest.
"S Udaltsov has not lived where he is registered for a long time and his mobile phones are often turned off, strongly complicating the summoning of the accused by the investigator," the committee said.
President Putin's critics accuse him of cracking down on dissent since his return to the Kremlin and say he has used the justice system to persecute his adversaries and the parliament to adopt laws aimed at stifling the opposition movement.
Mr Udaltsov said a court hearing over whether to put him under house arrest was due today and he expected it to endorse the Investigative Committee request.
"Unfortunately, this repressive politics is going on," he said."Naturally, their task is to limit my activity to a maximum extent."
He has been repeatedly detained during opposition protests, in what his supporters say is a tactic intended to hamper his activism.
On Thursday, another opposition activist was arrested over the protests in May 2012, bringing to 12 the total number of people detained and awaiting trial in connection with the events.
One person has already been convicted over the May unrest.
Law enforcement officials have also searched the offices of an anti-corruption organisation led by another prominent opposition figure, Alexei Navalny.