The Basmanny court remanded Shamil Burayev in custody until September 7, and Magomed Dimelkhanov and Ibragim Makhmudov until the end of August.
Politkovskaya, who gained international recognition for her criticism of the Kremlin and reports of military atrocities against civilians in the troubled Caucasus republic of Chechnya, was gunned down in an elevator in her Moscow apartment building in October 2006.
Prosecutors said last year that Burayev, ex-head of Chechnya's western Achkhoi-Martan District, obtained Politkovskaya's address from Lieutenant Colonel Pavel Ryaguzov, also accused of involvement in the murder, and passed it on to the Makhmudov brothers, Demelkhanov and other suspects.
A Russian chief investigator has claimed that fugitive tycoon Boris Berezovsky was behind the murder of investigative journalist Anna Politkovskaya, a respected daily said on Thursday.
In an interview published by the Izvestia newspaper on Thursday, Dmitry Dovgy, a chief investigator at the Russian Prosecutor General's Office, claimed that Berezovsky, who lives in London, ordered the murder of the well-known journalist and author of several books critical of Vladimir Putin.
Dovgy has recently been suspended from his post on suspicion of taking bribes totaling some $4.5 million. However, Izvestia said the interview was recorded before Dovgy was suspended.
Although he was unable to offer any proof to support his allegations, Dovgy said he was convinced that the murder had been carried out by "Boris Berezovsky, through Khozh-Akhmed Nukhayev," and that her death had been "advantageous" for the former Kremlin insider at that particular moment in time.
Khozh-Akhmed Nukhayev is "a fugitive Chechen criminal gang leader" also accused by the Russian government of ordering the murder of former Forbes editor Paul Khlebnikov in Moscow in 2004.
He also claimed that the murder was connected with Politkovskaya's "articles, as well as her personally."
Russian authorities announced last week that Politkovskaya's killer had been identified and placed on the country's 'most wanted' list.
Berezovsky dismissed the accusations in an interview with Ekho Moskvy radio.
"This is another attempt to distract the investigation from searching for the real person behind the murder," the tycoon said.
Twelve criminal investigations have so far been launched in Russia against Berezovsky, a one-time close associate of the late president Boris Yeltsin, and he also faces a criminal probe in Brazil.
The businessman has also been accused of plotting to stage a coup in Russia, as well as embezzling $13 million from a leading Russian bank. These two cases were opened in the spring and summer of 2007, respectively.
Russia has issued multiple warrants for Berezovsky's arrest and has repeatedly demanded that the U.K. extradite him. Berezovsky, a business partner of George Bush's brother, Neil Bush, has been granted political asylum in Britain.