UPDATE 2-Russia orders retrial in Politkovskaya murder case

* Court orders retrial of three accused of helping murderer

* Politkovskaya's son says retrial is a waste of time

(Adds reaction from son, lawyers, prosecutors)

By Aydar Buribayev

MOSCOW, June 25 (Reuters) - Russia on Thursday said it would retry three men acquitted earlier this year of being accomplices to the murder of journalist and Kremlin critic Anna Politkovskaya who was shot dead at her apartment block in 2006.

However, her son Ilya rejected the Supreme Court's decision and said a retrial would delay efforts to find the gunman and mastermind of the murder, the most high-profile in a spate of reporters' killings in Russia.

The Supreme Court judge ordered the "the sentence ... cancelled and the criminal case sent for a new hearing in the same court," accepting the state prosecutor's claims the trial was riddled with procedural violations.

After a four-month trial, a jury ruled in February brothers Dzhabrail and Ibragim Makhmudov were not guilty of acting as accomplices in the murder and cleared former police officer Sergei Khadzhikurbanov of organising the crime.

A different judge and jury will now hear the case, which will feature the same evidence as the first trial, said prosecutor Yulia Safina.

Politkovskaya, a 48-year-old mother of two who published scathing exposes of official corruption and rights abuses, was shot as she returned to her central Moscow apartment block from a Saturday afternoon shopping trip on Oct. 7, 2006.

No one else has been charged for the murder.

Observers consider the case a test of Russia's justice system and resolve to protect freedom of speech.

Her family have said they do not want a retrial with the same evidence, saying it will sap resources from efforts to find the mastermind of the killing.

"I think there should not be a repeat trial. The case should be sent by the court for additional investigation," said Politkovskaya's son Ilya. Asked if the new trial would hamper efforts to find the killer, he said "yes."

Anna Stavitskaya, who represents Politkovskaya's family, said: "We did not challenge the acquittal. We did not think it needed to be overturned.

"We do not want the case to be brought to a standstill."