* Supreme Court had thrown out 2009 acquittal
* Activists say no justice until those behind killing found
* Murder drew attention to risks of challenging Kremlin (Adds quote, details, context)
By Steve Gutterman
MOSCOW, May 20 (Reuters) - Five men were convicted on Tuesday of murdering 2006 of investigative journalist and Kremlin critic Anna Politkovskaya, including three defendants who had been acquitted in a previous trial.
Politkovskaya's killing drew attention to the risks faced by Russians who challenge the authorities and deepened Western concerns for the rule of law under President Vladimir Putin, who was then serving his second term.
Another jury's 2009 acquittal of three of the men who were found guilty of murder on Tuesday embarrassed Russian prosecutors and was later thrown out by the Supreme Court, which ordered a new trial.
The defendants were three Chechen brothers, one of whom was accused of shooting Politkovskaya in the lobby of her Moscow apartment building on Oct. 7, 2006, as well as their uncle and a former police officer.
The convictions are a victory for Russian prosecutors and the state, but rights activists and relatives of Politkovskaya say that justice will not be done until those who ordered her contract-style killing are identified and convicted.
"The murder will only be solved when the name of the person who ordered it is known," a lawyer for Politkovskaya's family, Anna Stavitskaya, was quoted as saying by RIA news agency.
She welcomed the jury's verdict but said the men found guilty "are only a few of the people who should be brought to justice", RIA reported.
A spokesman for the federal Investigative Committee, Vladimir Markin, said the authorities were doing all they can to identify and track down the person behind the killing, Russian news agencies reported.
Kremlin critics say they doubt that will ever happen because of suspicions the trail could lead too close to the government.
Politkovskaya, a reporter for Novaya Gazeta who was 48 when she was shot dead while returning home after shopping for groceries, was best known for her dogged reporting on human rights violations in the North Caucasus province of Chechnya.
Lawyers for the defendants - Rustam Makhmudov, his brothers Ibragim and Dzhabrail, their uncle Lom-Ali Gaitukayev, and former Moscow police officer Sergei Khadzhikurbanov - said they would appeal.
Investigators say Gaitukayev organized the logistics of the killing while in jail for another matter, while Khadzhikurbanov was in charge of preparing for the slaying and Ibragim and Dzhabrail Makhmudov helped track her.
Ibragim and Dzhabrail Makhmudov and Khadzhikurbanov were previously acquitted.
The five men will be sentenced by a judge at a later date and could face life in prison. Prosecutors will recommend sentences at a court session on Wednesday, RIA reported.
(Writing by Steve Gutterman; Editing by Mark Heinrich)