Memorial says decision prompted by murder of prominent activist Natalia Estemirova.
Politkovskaya’s family and their lawyers have repeatedly called for the entire case to be sent back to the prosecutors’ office for a new investigation.
Politkovskaya, who was sharply critical of Vladimir Putin, Russia’s prime minister, and his policies in Chechnya, was gunned down in the stairwell of her apartment building on October 7, 2006 in an apparent contract killing.
The investigation into her death has long been criticised by human rights groups.
Karinna Moskalenko, a lawyer for the Politkovskaya family, said: “The sole problem in this case is that the crime has not been solved and the investigation is incomplete.
“Only the prosecutors can eliminate the problems that we saw in the previous trial and we are seeing again in this trial.”
Amalia Ustaeva, a prosecutor, agreed that the case into the three suspects could be returned to the prosecutors’ office and integrated with the probe into the suspected killer and the unknown mastermind.
“I suggest that for the full investigation of the criminal case, the two cases can be combined,” she said.
Of the suspects, Chechen brothers Dzhabrail and Ibragim Makhmudov are accused of acting as drivers at the murder scene for the killer, who prosecutors say was a third brother, Rustam, who is still at large.
Sergei Khadzhikurbanov, a former police investigator, is charged with providing logistical assistance for the killing.
Politkovskaya had written dozens of articles for her Novaya Gazeta newspaper and a book called Putin’s Russia accusing the former president of using the Chechen conflict to strangle democracy in the country.
The murder last month of Natalya Estemirova, a prominent Russian rights activist who worked with Politkovskaya to investigate abuses by Russia forces in Chechnya, has again brought the case to the fore.
Politkovskaya relied on Estemirova as a source and co-investigator in many of the acclaimed reports detailing horrific abuses during the Kremlin’s war in Chechnya.
“This atmosphere of impunity is responsible for the amount of crimes against journalists,” said Dmitry Muratov, the editor-in-chief of Novaya Gazeta.
“The situation is paradoxical in Russia: the assassins of journalists feel closer to power than the journalists themselves.”