A police statement said detectives would seek to trace Gaidar's movements before he fell violently ill during a conference in Dublin on November 24.
Gaidar's spokesman, Valery Natarov, says his boss is feeling better.
"There is no danger for his life, as the doctors say, and the health condition of [Gaidar] is improving," Natarov said.
Doctors in Moscow, where Gaidar is now recovering, said on November 30 that they saw no natural cause for his ailment.
His daughter says her father could be released from hospital as soon as next week.
(Reuters, AFP)