MOSCOW, Russia (AFP) – Russian President Vladimir Putin lifted a little of the secrecy around his grandchildren and mockingly offered ex-FBI chief James Comey asylum during his annual televised phone-in on Thursday.

But the Kremlin strongman ignored more biting questions from viewers about jailed opposition leader Alexei Navalny and his plans to stand for a fourth term, which appeared on-screen in an apparent glitch.

In comments aimed at a domestic audience, Putin insisted the latest US sanctions over alleged election meddling are efforts to "contain Russia".

The US Senate voted overwhelmingly to approve further sanctions against Russia on Wednesday.

"The United States is not our enemy," Putin said, but he complained of Russia facing sanctions "throughout all of our history" from global partners who fear a "serious competitor".

Putin also jokingly suggested he could offer political asylum to fired FBI director James Comey -- who had been overseeing the bureau's Russia investigation -- comparing him to fugitive NSA whistle-blower Edward Snowden, who has asylum in Russia.

Putin spoke after Comey said he had arranged for notes on his one-on-one meetings with Donald Trump to be leaked to a reporter.

"When the head of a security service records a conversation with the commander-in-chief and passes it to the media... then how is the FBI director different from Mr Snowden?" Putin asked. "If he is persecuted, we would be ready to offer him asylum in Russia. He should know this."

In an apparent glitch in the carefully choreographed live show, the screen displayed some rather caustic questions from viewers sent in by text message.

"Putin, do you really think people believe this circus with staged questions?" asked one viewer. Another question referred to jailed opposition leader Navalny, whose video accusing Prime Minister Dmitry Medvedev of massive corruption has been viewed 23 million times on YouTube.

"Is true that Navalny is making a film about you now?" it asked.

Several called for an end to Putin's rule, ahead of elections next year when he is widely expected to stand for a fourth term, and compared him with Soviet leader Leonid Brezhnev who was in power for 18 years.

One message said simply: "Goodbye, Vladimir Vladimirovich."

Asked about the recent anti-corruption opposition protests organised by Navalny, Putin vaguely dismissed "those who use existing difficulties for their publicity" and argued that Russians are less concerned about corruption today than several years ago.

In a cautious lifting of the veil on his closely-guarded personal life, he revealed to Russian media for the first time that he has grandchildren, while saying he wants to keep them out of the spotlight so they can grow up "normally".

The president earlier talked of having grandchildren to film director Oliver Stone in a documentary released this month in the United States but not yet shown in Russia.

On the phone-in show, Putin said that one grandson was born recently, to applause in the studio, while another is "already in preschool".

"The thing is, I don't want them to grow up like hereditary princes, I want them to grow up to be normal people," Putin said in explaining the secrecy around his family.

"If I mention ages and names, they would be identified and never left alone." Otherwise it was business as usual with Putin talking to young mothers in poor housing, hard-hat manual workers, and being introduced to a swaddled newborn baby by a doctor.

The president admitted the number of Russians living in poverty has grown in recent years while noting that "the recession has ended" and the economy has seen "modest" growth over the last three quarters.

According to official statistics, last year almost 19.8 million Russians were living below the poverty line -- 13 per cent of the population.