Russian opposition leader Alexei Navalny was laid to rest in Moscow on Friday, surrounded by crowds of mourners who chanted his name and blamed authorities for his death in prison.

Outside the cemetery where he was buried, some supporters shouted in grief while others yelled out slogans against the Kremlin and its offensive in Ukraine.

Despite a heavy police presence and official warnings, thousands of mourners paid their respects to the 47-year-old anti-corruption campaigner whose death in an Arctic prison was announced on February 16.

Navalny's death has been widely condemned by Western leaders and his allies have accused President Vladimir Putin of responsibility and of trying to prevent a dignified public burial.

The Kremlin, which has dismissed the accusations as "hysterical," warned against "unauthorised" protests around the funeral.

Navalny's body first lay in an open casket in a packed church in Maryino, southern Moscow, for a ceremony attended by his parents.

The coffin was closed immediately after the service, meaning many mourners who had wanted to file past were not able to pay their last respects at the Mother of God Quench My Sorrows church.

It was transported to the Borisovo cemetery, near the banks of the Moskva River, where several large wreaths were arranged around the grave.

"We won't forget you!", "Forgive us!" some mourners shouted as the coffin arrived.

Rights monitoring group OVD-Info said police had arrested at least 128 people attending tributes to Navalny in 19 cities across Russia on Friday.

"Any unauthorised gatherings will be in violation of the law and those who participate in them will be held responsible," Kremlin spokesman Dmitry Peskov said, according to TASS news agency.

"What are they afraid of? Why so many cars?" asked one mourner, Anna Stepanova, outside the church.

"The people who came here, they are not scared. Alexei wasn't either."

German Chancellor Olaf Scholz praised the thousands who turned out as "courageous" and French President Emmanuel Macron also paid tribute to the "courage" of those who went to pay their last respects.

The French, German and US ambassadors were seen among mourners outside the church, as were some of Russia's last free independent politicians.

Music from "Terminator 2" – Navalny's favourite film – was played as the coffin was lowered, his spokeswoman Kira Yarmysh said. (AFP)