"We do not want to burn any bridges, but if someone perceives our good intentions as indifference or weakness and intends to blow up these bridges, then they must know that Russia's response will be asymmetric, swift and harsh, " he said.
Addressing the Federal Assembly, Putin said "the meaning and content" of Russia's policy in the worldwide arena is "to ensure peace and security for the well-being of our citizens, for the stable development of the country".
OVD-Info, a group that monitors protests and detentions, said that almost 300 people had been detained over the rallies in dozens of different places.
Alexey Navalny's doctors were again denied access to the jailed Kremlin critic despite growing concern over the hunger-striking Russian opposition figure's failing health. "I hope that no one will think of crossing a "red line" with Russian Federation". "And where this line will be, in every particular case, we will determine it ourselves".
Putin backed claims by Belarusian President Alexander Lukashenko that his security services had thwarted an alleged USA plot to assassinate him, suggesting senior United States officials were involved in a "coup attempt" and accusing the West of pretending "that nothing is happening".
Putin's government is already a major focus of US foreign policy.
Russian President Vladimir Putin attends a meeting with his Belarus President Alexander Lukashenko in Saint Petersburg on April 3, 2017.
Mr. Putin began his state-of-the-nation speech by hailing the nation's response to the coronavirus pandemic.
Vladimir Putin lauds Russia’s vaccine work
He vowed that Russian Federation, one of the world's major producers of oil and gas, would do its part to fight climate change, setting a target for the country's emissions to be "less than in the European Union". Putin announced new social support measures for families with children ahead of a September parliamentary election.
Mikhail Khodorkovsky, the former oil tycoon who spent 10 years in custody after falling out with the Kremlin, publicly called on Russians to join the protests in a Twitter post.
Security forces had issued a warning against taking part in "illegal gatherings" and appeared to be moving quickly to deter protesters.
His lawyers and allies are demanding he be transferred to a regular hospital, but the Kremlin has said Navalny is not entitled to special treatment.
Spokeswoman Kira Yarmysh said she was also detained at the entrance to the building, while independent monitor OVD-Info said police had conducted searches and detained at least 53 people in 27 cities.
The politician, who is Putin's most persistent critic and was poisoned with a chemical nerve agent previous year, started a hunger strike three weeks ago to protest what he said was inadequate medical treatment and officials' refusal to allow his doctor to visit him.
Russia's prison service, which has repeatedly prevented Navalny's doctors from visiting him, said Monday that he had been moved from his penal colony in the Vladimir region some 100 kilometres (60 miles) east of Moscow to a medical facility at another colony in the same region.
Almost three weeks into the hunger strike, his doctors over the weekend warned that Navalny's health was failing so rapidly he could die at "any minute", as the United States threatened Russian Federation with "consequences" in the event of his death.
15-year-old girl fatally shot by police in Ohio
In a video circulating on Twitter that afternoon, three white officers allegedly taunted residents by saying "Blue Lives Matter". Police also are expected to release more body camera footage of the shooting on Wednesday, reports say.