In a post on X, Kira Yarmysh the spokeswoman thanked everybody who had demanded that the authorities hand over his remains.
"The funeral is yet to take place," she wrote.
Navalny's mother Lyudmila had reportedly been told to agree to a "secret" burial. If she refused, he would be buried at the prison colony where he died.
She has spend the last week in the town close to the prison where he died, trying to first confirm the location of his body then demanding it be returned to her.
After signing a death certificate saying he had died of natural causes, she was then given three hours to agree to a "secret" funeral for her son.
If she didn't agree he would be buried within the grounds of the prison where he died, Ms Yarmysh said his mother was told.
However, Lyudmila had apparently refused to negotiate with the authorities.
In a video recorded before the release of the body, Navalny's widow Yulia Navalnaya accused "demonic" Russian President Vladimir Putin of "torturing" the corpse of a political opponent.
Navalny's allies urged supporters "not to relax" and his spokeswoman, Kira Yarmysh, wrote on X there was no certainty that Russian authorities would let the relatives hold a funeral "the way the family wants and the way Alexei deserves."
In her six-minute video published on YouTube, Navalnaya said she would continue the fight against Putin's regime, questioned the president's faith and accused him of holding her husband's body "hostage".
On Friday Navalny's mother Lyudmila said that Russian investigators were refusing to release his body from a morgue in Salekhard until she agreed to lay him to rest without a public funeral.
She said an official had told her that she should agree to their demands, as Navalny's body was already decomposing.
On Saturday, Navalny aides said thorities had threatened to bury him in the remote prison colony where he died unless his family agreed to their conditions.
Navalnaya said her husband had been a devout Christian, who attended church and had fasted for Lent even while in prison. She said his political activism had been inspired by Christian values.