Navalny's wife shows up to support protesters in Moscow

"Yulia! Yulia!" the crowd chanted as the jailed critic's wife milled about protesters.

Protesters in central Moscow also chanted, "Freedom to Navalny!" and "Let the doctors in!."

Police rounded up more than a thousand protesters on Wednesday as Russians in dozens of cities took part in rallies organized by allies of hunger-striking Kremlin critic Alexei Navalny over his failing health in jail.

His spokeswoman was jailed for 10 days, and another close ally detained, on the same day that President Vladimir Putin delivered a state-of-the-nation speech warning the West not to cross Russia's "red lines" and pointedly made no mention of Navalny.

"This is one of the last gasps of a free Russia, as many are saying. We came out for Alexei ... against a war in Ukraine and the wild propaganda," said Marina, a student at the Moscow protest.

OVD-Info, a group that monitors protests and detentions, said 1,004 people had been arrested, including 351 in St. Petersburg and 87 in the Urals city of Ufa.