In 2014, a court finally sentenced two men to life in prison for Politkovskaya's murder, and handed lengthy prison terms to three others involved in the killing.
But 12 years on investigators have yet to identify who ordered the apparent contract killing, and Novaya Gazeta said on Sunday the authorities had no interest in pursuing the investigation any further.
"Investigators are not replying to queries, they are not in touch with the complainant," said Sergei Sokolov, Novaya Gazeta's deputy editor.
On Sunday, her newspaper published a long list of questions it said remained unanswered.
Novaya Gazeta asked why Lom-Ali Gaitukayev, a Chechen who was found guilty of organising the hit, died last year in a penal colony where he was serving a life sentence.
His nephew Rustam Makhmudov, who fired the fatal shots, is serving a life term.
"No one knows what is happening with the search for the mastermind and others involved in this," the newspaper said.
The judges found that Russian investigators should have explored possibilities that the crime was ordered by "agents of Russia's FSB domestic secret service or of the administration of the Chechen Republic".
Politkovskaya's supporters were set to stage memorial events in Moscow and other cities.
She won numerous awards for her reports and books, and several awards were established in her name.
On Thursday, the Reach All Women in WAR Anna Politkovskaya Award, set up to recognise women promoting human rights in war zones, was bestowed on Indian activist Binalakshmi Nepram and Belarus' Svetlana Aleksievich, the 2015 winner of the Nobel prize for literature.
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