Russians have gone to the polls in local elections after weeks of opposition protests that led to the biggest police crackdown on dissent in nearly a decade.

Although municipal and regional polls were held across the vast country, most attention has been focused on the vote in Moscow, where independent would-be candidates and their supporters have been arrested and jailed and large protests were held over the summer.

About 7.2 million people were eligible to elect 45 lawmakers in the Moscow parliament, which is dominated by the ruling United Russia party. Not a single candidate is formally running on the United Russia ticket as the party’s popularity has hit rock bottom.

Alexei Navalny, the most prominent of Russia’s opposition leaders, was hoping to take advantage of the discontent by calling on supporters to back his “smart voting” strategy and cast ballots for the candidate with the best chance of defeating a pro-Kremlin candidate. “Today we are fighting to destroy United Russia’s monopoly,” Navalny told reporters after voting in the capital.

Analysts say the vote is a test run ahead of parliamentary elections due in 2021 – both of the opposition’s ability to mobilise support and the authorities’ willingness to tolerate dissent.

Outside a polling station in Moscow’s Gagarinsky district there were more police officers than voters on Sunday.

Lyubov Sobol, an anti-corruption campaigner, on polling day. Photograph: Shamil Zhumatov/Reuters

“Russia is not developing, we are trapped under layers of corruption,” said Yulia, 32, who did not want to give her last name. “I have come here today to change that. I voted for the communist in order to split the vote for United Russia.”

Vadim Turinov, 42, an IT consultant, was dismissive of the “smart-voting” plan. “Why vote at all? These local elections do not matter at all,” he said.

Activists alleged multiple incidents of wrongdoing at polling stations across the country, including ballot stuffing. Vladimir Yegorov, a monitoring group coordinator, was arrested on Saturday night. In the city of Penza, several observers were detained ahead of the election and released without further explanation.

Putin voted at his usual polling station at the Russian Academy of Sciences, where he appeared to dismiss the opposition’s concerns about barred candidates. “In some countries you have 30, 50, or 100 [candidates],” he told reporters. “This doesn’t change the quality of their work. It’s quality not quantity that’s important.”

Lyubov Sobol, 31, a lawyer for Navalny’s anti-corruption fund who was barred from running, said Sunday’s vote showed authorities had given up pretending that elections in Russia were democratic. “This is the funeral for even the semblance of democratic elections,” said the lawyer, who was a key protest leader.

United Russia, formed in 2001 to support Putin, has seen its popularity collapse in recent years as incomes have fallen under western sanctions.

Konstantin Gaaze from the Carnegie Moscow Center said the economy would ultimately decide Putin’s fate. “His approval rating declines when the economy does badly,” Gaaze said. “Putin’s biggest problem is that he has failed to fight poverty.”

Agence France-Presse contributed to this report