Russia's deputy prime minister on Saturday demanded an apology from protest leader and top Kremlin critic Alexei Navalny after he alleged massive corruption in an arms procurement deal.

The chief critic of President Vladimir Putin claimed Friday in his corruption-busting blog that the defence ministry had announced a tender to buy Glock pistols at a price he called four times the market rate.

The ministry procurement agency was set to buy "ordinary pistols for the price of gold ones," he wrote.

Deputy Prime Minister Dmitry Rogozin, who oversees the defence sector, on Saturday demanded an apology.

He denied the allegations, writing on his official Twitter account that: "Navalny will have to apologise."

Rogozin's response was a rare acknowledgement by the government of the existence of Navalny, who cemented his reputation by speaking at protest rallies against Putin's return to the Kremlin.

Putin never refers by name to the charismatic 37-year-old lawyer who coined the slogan "Putin is a thief."

Navalny has published online exposes of official corruption that have forced several lawmakers to stand down.

Russia's defence ministry has been rocked by highly damaging corruption scandals, with Putin firing the previous defence minister amid a probe into a huge illegal property scheme.

Navalny called for Rogozin and Defence Minister Sergei Shoigu to investigate the Glock tender.

He also questioned Rogozin's position, mentioning that Rogozin's son used to hold a senior post in a company selling Glock pistols in Russia.

"I have been consistently putting order in the arms sector and will not give anyone a reason to doubt my personal integrity," Rogozin wrote on Twitter.

He said he had ordered a check into the tender before Navalny published the claim.

He added that his son had left his post because of such "idiotic questions" and that he and his family had no shares in the company.

Navalny last month came second in Moscow mayoral polls against an incumbent close to Putin, despite facing the threat of a jail in a long-running trial.

The protest leader returned to Moscow a free man last week after a court in the northern Kirov region suspended his five-year penal colony sentence in a fraud case.

But the court upheld his conviction for embezzlement over the sale of state-owned timber, and the sentence still bars him from standing for political office.

Rogozin referred contemptuously to Navalny's conviction, saying: "As for Navalny, he needs to work on his wood-related problems. I on the other hand look after my reputation."