Sympathizers of the militant group hail the attack as a reaction to Belgium's "war" on religion.
Alexey Pushkov has told NATO to focus on suicide bombers, not Russia.
Djordje Djokovic was coming in to land when explosions hit Zaventem airport.
European shares fell sharply in the wake of the attacks at Brussels airport and a metro station in the capital.
Gatwick, Paris and Frankfurt airports increase security levels after two explosions hit Brussels check-in area.
No links to extremism yet established but ISIS suspects remain at large in Belgian capital.
Shots were fired and Arabic was shouted before the blasts at Zaventem airport, according to reports.