At least eight foreign nationals were among the 35 people killed in the suicide bomb blast that ripped through Moscow's busiest airport.
The bomber detonated the device in the international arrivals hall at the airport, causing scenes of chaos and carnage.
The bomb sent shrapnel, screws and ball bearings ripping through the air.
Russia's Emergencies Ministry said eight foreign citizens, including two Britons, were among those killed.
No claim of responsibility has been made for the blast at Domodedovo Airport, which left another 110 injured.
But Chechen militants behind many other terrorist acts in Russia, including last year's double suicide bombing on the Moscow subway that killed 40, are the main suspects.
President Medvedev ordered security at Moscow's two other commercial airports and other key transport facilities to be put on high alert.
Reports on Russian television suggested that the suspected bomber was carrying a suitcase and shouted "I'll kill you all!" before detonating the device in the passenger-filled hall.
The Interfax news agency also cited law enforcement sources saying the head of the bomber had been found on the blood-spattered floor.
Eyewitness Artyom Zhilenkov, a 35-year-old driver, said: "I saw the suitcase, the suitcase was on fire."
He added: "The guy standing next to me was torn to pieces."
Witness Mark Green said: "As we were picking up the bags to put them into the back of the car, there was an almighty explosion. It reverberated through our bodies."
Another Briton Jeremy Spencer, who was on a BA flight which landed around 45 minutes before the fatal blast, was less than 100 metres away from the spot where the bomb exploded.
Describing the moment the device detonated, he said: "There was a very loud boom that shook the floor and ceiling and then there was dust falling down from the ceiling.
"We were told it was a car bomb by some fellow travellers, but initially I thought it was a construction accident as there was some work being done inside the terminal."
Footage posted on YouTube showed the aftermath of the incident, with a mass of bodies and luggage strewn on the floor of the smoke-filled terminal.
According to reports, Russian police were today attempting to trace three men in connection with the incident.