Some German politicians and media have already blamed Moscow for the assassination of 40-year-old Georgian national Zelimkhan Khangoshvili -- though Russia denies the claims.
Khangoshvili was shot twice in the head at close range in Berlin's Kleiner Tiergarten park on August 23, allegedly by a man on a bicycle who was later seen throwing a bag into a river.
German police arrested the man, saying he was a 49-year-old Russian national named only as Vadim S.
However, the investigative website Bellingcat reported on Tuesday that the man was using a fake identity.
It said he was 54-year-old Vadim Nikolaevich Krasikov and that he grew up in Kazakhstan when it was part of the Soviet Union before spending time in Siberia.
The site said he had previously been accused of murdering a Russian businessman in Moscow in 2013 in which the attacker also used a bicycle to approach the victim.
Russia put Krasikov on an Interpol wanted list but later withdrew his name and "facilitated the issuance of a new, false identity for him", Bellingcat said.
German media said the suspicion was that Russian intelligence agencies had recruited him.
"The Federal Prosecutor's Office suspects Russian state agencies of having commissioned the murder," Der Spiegel said, adding that federal prosecutors were preparing to take over the case "in the coming days". Other outlets carried similar claims.
A spokesman for the federal prosecutor's office told AFP they were not currently in charge of the case and a foreign ministry spokesman declined to comment.
Fought against Russian forces
The killing has been compared with the poisoning of former Russian agent Sergei Skripal in Britain last year, widely blamed on Russian intelligence.
Relations between Britain and Russia plunged into a deep freeze after the incident.
Der Spiegel, in a joint inquiry with Bellingcat and The Insider, another investigative website, earlier detailed the evidence pointing to Russian secret services involvement in Khangoshvili's killing.
Their investigation also suggested the government of the Russian republic of Chechnya, led by Vladimir Putin ally Ramzan Kadyrov, might have been involved.
Bellingcat said the victim had fought for the Chechens in the second Chechen war in 1999-2002, then continued supporting Chechen separatists from his native Georgia.
He "recruited and armed" a volunteer unit to fight Russian troops in Georgia in 2008, it added.
After surviving two assassination attempts in Georgia, he had spent recent years in Germany and applied for asylum.
Der Spiegel said police had recovered an air ticket from the suspect for Moscow for the day after the attack and a large sum of cash in his apartment.
The man has been charged with murder but has reportedly refused to speak to investigators.
The joint media investigation said that he had a valid passport but no such person existed in Russia's national citizen database.
The suspect's passport number had been traced back to a unit of the Russian interior ministry, which was known to have delivered identity documents for Russian military intelligence.
Putin's spokesman Dmitry Peskov said in the days after the killing that it had "nothing to do with the Russian state".