Grishchenko was commenting on Tuesday's article by the London newspaper The Guardian, which said that Russian intelligence services were sheltering Bosnian Serbs indicted by the ICTY, including Gojko Jankovic, who surrendered to the tribunal on Monday.
The ambassador said that Russian prosecutors, based on information from The Hague, had already given instructions "to some bodies".
Asked if the Russian government knew that Jankovic had stayed in Russia for several years, Grishchenko said it had not, "because if it had, it would have been another story".
"It is not easy to find a person in a large country. Judicial authorities are looking for dozens and hundreds of our citizens and we have been unable to track them down for years," the ambassador said.
Grishchenko said that the information that Jankovic had spent several years in Russia could be credible.