MOSCOW (Reuters) - Five men on trial for murdering Russian investigative reporter Anna Politkovskaya, an ardent critic of President Vladimir Putin, pleaded not guilty on Wednesday in a court case that her family has decried as illegitimate.

Politkovskaya, who angered authorities by investigating high-level corruption and documenting human rights abuses by Russian forces in the North Caucasus, was shot dead in 2006 in the Moscow residential building where she lived.

Kremlin critics and rights campaigners say Russia's failure to jail all those responsible for the murder more than six years after it happened creates a climate of impunity for those who try to stifle opponents of Putin's government.

The trial is the second attempt to convict some of the defendants over the murder after a jury acquitted three of them in 2009. The Supreme Court later overturned this verdict at the prosecutors' request and referred the case back to them.

Politkovskaya's son Ilya and daughter Vera have denounced the trial as "obviously illegitimate" and are boycotting court proceedings.

"The fact that the victim's side is not taking part in the trial does not prevent it from going on," a spokeswoman for the Moscow city court said.

All the defendants have pleaded not guilty, she said.

In the dock are three Chechen brothers - one of whom, Rustam Makhmudov, is suspected of having pulled the trigger - along with their uncle Lom-Ali Gaitulayev and a former policeman.

Politkovskaya was murdered on Putin's birthday on October 7 as she was returning home from a grocery store.

Putin condemned the murder at the time but also said Politkovskaya's ability to influence Russian politics had been "extremely insignificant" and that her killing caused greater damage to Russia's image than her writings.

Another former policeman has already been convicted in the case and sentenced to 11 years in penal colony, but his trial failed to reveal the person or people behind the murder.

(Reporting by Gabriela Baczynska; Editing by Raissa Kasolowsky)