Ralf Meyer said on German television that the investigative team had already asked its Russian colleagues to answer some questions, but received no response.
"Therefore, we have sent an official request to Russia through the German Federal Prosecutor's Office asking for help," Meyer said.
In Russia, Kovtun is being treated as a witness in the case of Alexander Litvinenko, an FSB defector and outspoken Kremlin critic who died November 23 of a fatal dose of radioactive polonium-210. He has been questioned by Russian prosecutors and Scotland Yard detectives, currently in Moscow investigating the high-profile case.
Russian prosecutors have said that Kovtun, who met with Litvinenko in London at around the time when he was poisoned, has been diagnosed with an illness caused by radiation poisoning and is in hospital.
But Meyer said German investigators suspect Kovtun, who has a residence permit in Germany, of having illegally transported nuclear materials.
Traces of radiation have been detected in Hamburg at several sites visited by Kovtun between October 28 and November 1, including at his ex-wife's and ex-mother-in-law's apartments.
His ex-wife, two children and her boyfriend were hospitalized Monday with suspected radiation poisoning. But doctors diagnosed no serious poisoning, saying the patients were fine but "suffering from serious psychological stress."