MOSCOW—Chanting slogans against President Vladimir Putin, tens of thousands took to the streets Sunday across Russia to demand the release of jailed opposition leader Alexei Navalny, keeping up nationwide protests that have rattled the Kremlin. More than 4,000 people were detained by police, according to a monitoring group, and some were beaten. Russian authorities mounted a massive effort to stem the tide of demonstrations after tens of thousands rallied across the country last weekend in the largest, most widespread show of discontent that Russia has seen in years. Yet despite threats of jail terms, warnings to social media groups, and tight police cordons, the protests again engulfed many cities on Sunday. The 44-year-old Navalny, an anti-corruption investigator who is Putin’s best-known critic, was arrested on Jan. 17 upon returning from Germany, where he spent five months recovering from a nerve-agent poisoning that he blames on the Kremlin. Russian authorities have …