But a government spokeswoman cautioned the plan had not been given final approval, amid objections from the Russian Orthodox Church.
A high-level government task force put forward a proposal for the burial to take place in Russia's former imperial capital on October 18.
The task force "will propose to the government the holding of a burial ceremony of the remains of Tsarevich Alexei and Grand Duchess Maria on October 18," it said after meeting on Friday.
She said that further consultations would be held, including with the Russian Orthodox Church.
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The task force proposed that the burial take place in the former imperial capital's Peter and Paul Cathedral, where Nicholas II, his wife and their three other children were buried in 1998.
"The Saint Petersburg authorities have drawn up the ceremony for all the events linked to the burial," Saint Petersburg's deputy governor Vladimir Kirillov told Interfax news agency.
But the powerful Orthodox Church, which has long delayed the funerals over doubts about the victims' identity, called for additional testing of the remains.
"It is very important that all possible new tests are carried out," Church spokesman Vsevolod Chaplin told Russian news agencies, saying "believers have many questions."
The Orthodox Church has canonised all the Romanov family, who were executed by the Bolsheviks, as martyrs.
It has so far refused to acknowledge the results of DNA identity tests by Russian criminal investigators.
The task force said that on the Church's request it asked investigators, forensic experts and geneticists to submit proposals for additional testing "if it were necessary to resolve any historical problems."
The remains have been stored in a repository, the State Archives, since their discovery.