New investigations into the 2006 murder of Russian journalist and Kremlin critic Anna Politkovskaya were ordered by Russia's Supreme Court Thursday, reversing a lower court decision from August, the Interfax news agency reported, according to dpa. Politkovskaya's family had appealed the August 7 decision by a Russian military court, which had ruled that no new evidence was needed in the retrial. The retrial was itself ordered by the Supreme Court after an appeal from the state prosecutor's office to overturn a previous acquittal against suspects in the case. A government spokesman confirmed the decision, which means the prosecutor's office is now charged with the new investigations. The prosecutor's office had also appealed the decision to block new investigations. Investigations into the suspected murderer, Chechen Rustam Makhmudov, who has not yet been found, must be taken into account in the current trial of the four other men accused of being accomplices, said a judicial spokesman. "The decision means we're one step closer to clearing up the case," said the Politkovskaya family's lawyer, Karina Moskalenko. "But it's important to remember that it's already been three years since the murder took place." A spokesman for the state prosecutor's office warned that expectations should not be raised too high. "We will go over the charges thoroughly," he said. "But much depends on finding Makmudov." The four men on trial face charges as accomplices in the contract- style slaying in Politkovskaya's Moscow apartment block on October 7, 2006. They were freed in February due to lack of evidence. In the initial trial, prosecutors had accused two brothers of the suspected murdered Rustam Makmudov, Dzhabrail and Ibragim Makhmudov, of being accomplices and former police officer Sergei Khadzhikurbanov of helping the killer get away. The fourth defendant, Pavel Ryaguzov, was acquitted in a separate case. Ryaguzov, an agent of Russia's FSB security service, was accused of providing the killer with Politkovskaya's address. The identity of those who had ordered Politkovskaya's killing is still unknown. The editor of "Novaya Gazeta" and ex-colleague of Politkovskaya Dmitri Muratov said that he hoped that the crime would now be more "thoroughly investigated." "There aren't enough pieces of the puzzle yet to build up a complete picture of what really happened," he said. Politkovskaya had reported on war crimes in the southern Russian republic of Chechnnya before she was shot dead in front of her Moscow flat on October 7, 2006, at the age of 48. Her family and colleagues believe the murder was politically motivated. Politkovskaya, who had won many international prizes for her work, was a vocal critic of Kremlin policy in the North Caucasus. Opponents of the government in Moscow suspect it of being involved in the crime and consequently not interested in clearing it up. Human rights activists complain that hardly any of the politically motivated murders of journalists have been solved. In July 2009 a friend of Politkovskaya, Natalia Estemirova, was kidnapped and shot dead in Chechnya. The murder also remains unsolved.