A Russian court has imposed jail terms ranging from six to 18 years against seven left-wing campaigners after finding them guilty of "terrorism" charges.

Kremlin critics decried Monday's ruling, saying the activists had been framed and some tortured.

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The men, aged 23 to 31 and mostly from the provincial city of Penza, were accused of planning attacks against the 2018 FIFA World Cup and presidential election as part of an underground anarchist group called "the Network".

Other charges included drug dealing and weapons possession.

They had all denied the charges, and some said they were tortured in custody to produce confessions. Dozens of their supporters chanted "shame" in the military court in Penza as it handed down its ruling.

The Kremlin said President Vladimir Putin was aware of the case, but that it would not be appropriate for him to intervene in it.

"The president has repeatedly looked into this situation and repeatedly ordered everything to be checked thoroughly to make sure everything is in line with the law," Kremlin spokesman Dmitry Peskov told reporters.

Opposition leader Alexei Navalny described the sentences as "horrific" in a post on Twitter.

"These very young people's testimony about an imaginary terrorist organisation were beaten out using torture. Any minister in the Russian government is 10 times more of a criminal and a threat to society than these guys," he said.

Human rights organisation Memorial said the men were political prisoners, describing them as left-wing activists and anti-fascists.

Almost 50,000 people signed a petition demanding that the case be closed.