* Putin gives annual state-of-nation speech
* Warns West not to cross Moscow's red lines
* Supporters of jailed Kremlin critic Navalny rally
* Police detain nearly 300 protesters (Adds U.S. diplomat being summoned, speech and protest details)
By Gleb Stolyarov and Andrew Osborn
MOSCOW, April 21 (Reuters) - President Vladimir Putin warned the West on Wednesday not to cross Russia's "red lines", saying Moscow would respond swiftly and harshly to any provocations and those responsible would regret it.
At a time of acute crisis in ties with the United States and Europe, with Russian troops massed near Ukraine and opposition leader Alexei Navalny on hunger strike in jail, the Kremlin leader used his state of the nation speech to project a message of Russian strength and defiance in the face of outside threats.
"We want good relations...and really don't want to burn bridges," Putin told both houses of parliament.
"But if someone mistakes our good intentions for indifference or weakness and intends to burn down or even blow up these bridges, they should know that Russia's response will be asymmetrical, swift and harsh."
Russia would determine where its red line lay in each specific case, he said, comparing those who attack it to hyenas led by a tiger.
His comments came at the climax of a speech dominated by Russia's response to the COVID-19 pandemic and resulting economic hardship. Putin announced new social support measures for families with children ahead of a September parliamentary election.
He adopted a sterner tone when setting out foreign policy.
"In some countries, they have developed a highly unseemly habit of picking on Russia for any reason, and most often for no reason at all - a kind of sport," said Putin, standing alone on a vast stage flanked by white, blue and red national flags and a backdrop of a giant double-headed eagle.
"Organisers of any provocations that threaten our core security interests will regret what they have done like they've never regretted anything for a long time."
Putin, who is 68 and has dominated Russia for two decades, made no mention of Navalny. The opposition politician is ill in prison after starving himself for three weeks to demand access to his own doctors.
The rouble firmed after Putin's speech, with markets interpreting it as not escalating tensions with the West.
CONFRONTATION WITH WEST
Recent weeks have seen an intensification of confrontation between Russia and Western countries, which are alarmed by Navalny's worsening condition and by what they say is the massing of tens of thousands of Russian troops near Ukraine and in Russian-annexed Crimea.
Washington last week tightened sanctions on Russia over accusations of computer hacking and election interference, and the Czech Republic accused Moscow of a role in explosions at an arms depot in 2014. Both expelled Russian diplomats. Russia denied wrongdoing and responded with tit-for-tat expulsions.
Moscow summoned a senior U.S. diplomat on Wednesday and said 10 embassy staff it expelled last week had a month to leave and that it would be disclosing the details of other punitive measures it had promised soon.
Tensions are also strained over the fate of Navalny, whose supporters rallied across Russia on Wednesday in his support.
Two of Navalny's closest allies were arrested on Wednesday, their lawyers said. Lyubov Sobol, one of the faces of Navalny's popular YouTube channel, and Kira Yarmysh, his spokeswoman, were both detained in Moscow.
One Navalny aide, Ruslan Shaveddinov, tweeted: "Right now across the whole of Russia they are detaining potential protesters. This is repression. This cannot be accepted. We need to fight this darkness."
European Council President Charles Michel called the arrests "deplorable" and urged Russian authorities to respect people's right to assemble.
OVD-Info, a group that monitors protests and detentions, said that nearly 300 people had been detained over the rallies in dozens of different places. The figure was expected to climb.
The Russian government has said the gatherings are illegal. Previous pro-Navalny rallies have been dispersed by force, with thousands of arrests.
Four doctors from outside Russia's federal prison service visited Navalny on Tuesday and found his health to be satisfactory, Russian human rights commissioner Tatyana Moskalkova said.
In his speech, Putin urged all citizens to get vaccinated and predicted that Russia would achieve collective immunity by the autumn.
On the eve of an online climate summit to be hosted by U.S. President Joe Biden, Putin also called for tougher "polluter pays" rules and set a goal for Russia to cut its greenhouse gas emissions below those of the European Union in the next 30 years. (Additional reporting by Vladimir Soldatkin, Gleb Stolyarov, Tatiana Voronova, Olesya Astakhova, Oksana Kobzeva, Daria Korsunskaya , Elena Fabrichnaya, Ekaterina Golubkova, Andrey Ostroukh, Anastasia Lyrchikova, Gabrielle Tétrault-Farber, Tom Balmforth, Polina Ivanova, Anton Zverev and Anton Kolodyazhny; Writing by Mark Trevelyan/Andrew Osborn; editing by Timothy Heritage and Alistair Bell)