Germany has accused Russian Federation of failing to assist in the investigation.
From the outset, the "execution-style" killing of 40-year-old Zelimkhan Khangoshvili drew suspicion of Russian involvement.
In its statement on Wednesday (in German), the German federal prosecutor identified the victim as "Tornike K".
The suspect was riding a bicycle and was seen by witnesses afterwards throwing the bike and a stone-laden bag with a gun into a river. Prosecutors said he also went by the alias Vadim S., and German and worldwide news outlets have reported he had links to organized crime in Russian Federation. "The foreign ministry has today declared two employees of the Russian embassy in Berlin as personae non grata with immediate effect", the ministry said in a statement.
Leonid Slutsky, the head of the Russian Duma (parliament) foreign affairs committee told Interfax news agency that the expulsion of two diplomats was an unfriendly step.
The investigative website Bellingcat said yesterday the suspect in custody was using a fake identity.
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.
Russian Federation issued an Interpol global arrest warrant for Mr Krasikov in 2014, but withdrew it a year later without explanation.
Khangoshvili fought against the Russians during the Second Chechen War from 1999 to 2009, and worked thereafter in both Georgia and Ukraine against Russian interests, according to Deutsche Welle.
It also follows the poisoning of former Russian spy Sergei Skripal, and his daughter who were poisoned with a nerve agent on British soil past year.
He was a close ally of Chechen President Aslan Maskhadov, who masterminded Chechen guerrilla resistance to Russia and was killed in a Russian special forces raid.
Tsatieva said Khangoshvili escaped to Germany in 2016 after multiple attempts against his life in Georgia, but was denied asylum here.
Chechnya is now run by Ramzan Kadyrov, a former rebel who switched sides and is now fiercely loyal to Russian President Vladimir Putin.