Kremlin critic Alexei Navalny was arrested on Tuesday after breaking house arrest to join an opposition rally in Moscow, hours after a court gave him a suspended sentence for fraud. His brother Oleg was jailed for three and a half years for the same offence.

"Yes, there is this house arrest. But today I want to be with you. So I'm coming," Navalny said on his Twitter feed, posting a picture of himself in the Moscow metro, shortly before he was detained by police. After his arrest, he sent a tweet saying that he "had not got as far as the square".

"I call on everyone not to leave until they are forced to," he said. "They cannot arrest everyone".

An estimated 2,000 people braved bitter cold to attend the protest, with demonstrators chanting "Shame! Shame!" every time somebody was arrested.

In a case which critics say was politically motivated, the judge on Tuesday handed Navalny - Vladimir Putin's most high-profile opponent - a suspended three-and-a-half-year sentence. He had faced up to 10 years in jail. But in an unexpected move which stunned Russia's opposition, the court sentenced Oleg Navalny to a term behind bars.

Navalny's supporters said the Kremlin was returning to the sinister Soviet-era practice of punishing the relatives of those it disliked. Upon hearing the verdict, mumbled quietly by the judge, Yelena Korobchenko, Alexei Navalny rolled his eyes and looked at his brother.

Both men were found guilty of stealing 30m roubles (about £334,000 under the current exchange rate) from the French cosmetics company Yves Rocher. Asked by Korobchenko if the rulings against them were clear, Alexei replied: "Nothing is clear. Why are you imprisoning my brother? By this you punish me even harder."

The sentencing had originally been scheduled for 15 January, but was abruptly brought forward to the day before New Year's Eve, the main Russian holiday, in an apparent attempt to prevent large scale anti-Putin demonstrations. On Tuesday, riot police and military vehicles flooded Moscow's Manezh Square in anticipation of a major protest later in the day directly outside the Kremlin. The authorities have not given permission for the rally so it is considered illegal.

The European Union said the convictions eemed to be politically motivated, while calling for restraint during any protests against the verdict. "The guilty verdict delivered today ... against Alexei Navalny and his brother Oleg Navalny appears to be politically motivated," a spokeswoman for EU foreign policy chief Federica Mogherini said in a statement. "The EU stresses the importance of judicial decisions to be free from political interference, independent, and in full compliance with the rule of law," she added.

"Of all the possible types of sentence, this is the meanest," said Alexei Navalny outside court after his brother was taken away. "The government isn't just trying to jail its political opponents - we're used to it, we're aware that they're doing it - but this time they're destroying and torturing the families of the people who oppose them," he said.

Writing on his blog, Navalny said his brother's sentence would not stop him from political activity. He lambasted those at the top of Kremlin power as "thieves, scoundrels and traitors who must be destroyed". He also said ordinary Russians were guilty of allowing the political elite to plunder the country. "We let them through our passivity," he wrote.

Critics said the move was the latest attempt by the Kremlin to snuff out Navalny's long-running campaign against Putin. Navalny's friend, the opposition leader Ilya Yashin, said: "By taking his own brother as a political hostage, the sinister Kremlin wants to squash Navalny's spirit, so he shuts up."

Within hours of the court's decision, Moscow's political chatter was focused on one question: would putting your own family members in prison stop you from protesting against Putin? A majority of listeners tuning in to the liberal radio Echo of Moscow - 75 % - said it would not.

The radio's editor-in-chief, Aleksei Venedictov, described the Kremlin's new strategy against Navalny as "sophisticated torture". "The verdict is purely political. The Kremlin weakens Alexei by giving him thousands of little wounds. First they keep him for months under house arrest, forbid him to use the internet, then put him on trial, then throw his brother in jail - taking family members hostage is a sensational new strategy," Venediktov told the Guardian.

Oleg Navalny is the father of two small children and a former executive of the state-owned postal service. Unlike his better known brother, he has never played a role in the Russian opposition movement. His imprisonment in a penal colony seems to echo the Soviet-era practice of arresting the relatives of "inconvenient" people.

The court's decision quickly rippled to the cluster of Navalny's supporters waiting outside in the deep frost. It was a small gathering compared with the more than 100,000 people who attended the anti-Putin rallies that Navalny led only two years ago.

In 2013 he came second in Moscow's mayoral election, winning 27% of the vote. On Tuesday, however, many seemed more concerned with shopping for New Year parties.