The Kremlin said Monday the investigation into the death of Alexei Navalny was ongoing as it slammed "vulgar statements" over the Kremlin's responsibility for his death.

Russian authorities have so far refused to hand over the opposition leader's body to his relatives, enraging his followers who have accused the Kremlin of being "killers" trying to "cover their tracks."

President Vladimir Putin's spokesman Dmitry Peskov told reporters Monday an investigation was "ongoing" and that "all necessary actions are being carried out."

"At the moment, the results of the investigation have not been released, they are unknown," he said Monday.

Western leaders, including US President Joe Biden, have said Putin carries responsibility for Navalny's death.

"In these conditions, when there is no information, it is absolutely unacceptable to make such blatantly vulgar remarks," Peskov said Monday, without specifying which statements he was referring to.

Navalny, Putin's most vocal critic, died Friday aged 47 in the Arctic prison colony where he was being held on charges widely seen as punishment for campaigning against Putin.

Peskov said Monday he could not say when Navalny's body could be released to his family as it was not a matter for the president's office.

Navalny's team responded instantly to the remarks, repeating their charge that the Kremlin was trying to "hide their crime," in a post on Telegram. "Nothing is sacred to these scum," they added. (AFP)