Zelimkhan Khangoshvili, a 40-year-old Georgian national, was shot twice in the head in Kleiner Tiergarten park on August 23. A suspect was named as Vadim S but evidence revealed by German prosecutors indicated a possible fake identity.
Germany expelled two Russian diplomats on Wednesday after prosecutors said Moscow could be behind the killing of a former Chechen rebel commander in a Berlin park.
Zelimkhan Khangoshvili, a 40-year-old Georgian national, was shot twice in the head at close range in Kleiner Tiergarten park on August 23, allegedly by a Russian man who was arrested shortly afterwards.
The case has been compared with the poisoning of former Russian agent Sergei Skripal in Britain last year with a Soviet-era nerve agent, widely blamed on Russian intelligence.
The attempted murder plunged relations between Britain and Russia into a deep freeze, leading to tit-for-tat diplomatic expulsions.
After Germany's move on Wednesday, a Russian foreign ministry representative pledged "retaliatory measures".
"A politicised approach to investigation issues is unacceptable," said the representative, adding that Germany's statements were "groundless and hostile".
The suspect in the Berlin killing was said to be riding a bicycle and was seen by witnesses afterwards throwing the bike and a stone-laden bag with a gun into a river.
He has until now been named by police only as Vadim S but evidence revealed by German prosecutors on Wednesday indicated a possible fake identity.
"The foreign ministry has today declared two employees of the Russian embassy in Berlin as persona non grata with immediate effect," the ministry said in a statement.
"Despite repeated high-ranking and persistent demands, Russian authorities have not cooperated sufficiently in the investigation into the murder."
Federal prosecutors in charge of intelligence cases earlier on Wednesday said they had taken over the investigation.
"There is sufficient factual evidence to suggest that the killing...was carried out either on behalf of state agencies of the Russian Federation or those of the Autonomous Chechen Republic," the prosecutor's office said in a statement.
Chechnya has been led with an iron fist since 2007 by Ramzan Kadyrov, a close ally of Russian President Vladimir Putin.
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Outlining the results of their investigation so far, the statement said Vadim had travelled from Moscow to Paris on August 17 and then on to Warsaw on August 20.
He left his hotel in Warsaw on August 22 and his movements between then and the murder were unclear, it said.
Prosecutors said his visa for travelling to Europe indicated he was a civil engineer working for a company in Saint Petersburg.
But the company was not operational and a fax number for the firm was registered to another company belonging to Russia's defence ministry.
Prosecutors said the man's features matched those of a suspect in a 2013 murder in Moscow in which the suspect also approached the victim on a bicycle.
The investigative website Bellingcat on Tuesday said the suspect in both murders was 54-year-old Vadim Krasikov, who grew up in Kazakhstan when it was part of the Soviet Union before spending time in Siberia.
German media said the suspicion was that Russian intelligence agencies had recruited him after the 2013 killing.
Bellingcat said the victim had fought in the second Chechen war in 1999-2002, then continued supporting Chechen separatists from his native Georgia.
He also lived for a time under an assumed identity as Tornike Kavtarashvili, according to media reports.
Bellingcat said he "recruited and armed" a volunteer unit to fight Russian troops in Georgia in 2008.
After surviving two assassination attempts in Georgia, he had spent recent years in Germany and applied for asylum.