Putin did not elaborate. But the Interfax news agency reported that a composite sketch of the suspected male bomber - some reports say there was also a female bomber - suggested to investigators that he was from the North Caucasus, which forms Russia's southern flank.
The two assertions are not necessarily contradictory; other republics in the North Caucasus, some of which border on Chechnya, also have seen considerable unrest.
The implications of an attack originating somewhere other than Chechnya were not immediately clear. If the bomber or bombers were from neighboring Dagestan or Ingushetia - where militants and police have clashed before - it would represent a serious escalation of Russia's long struggle with Islamic separatists, but not a turn in an entirely new direction.
If, on the other hand, the bombing originated elsewhere - abroad by al-Qaeda, for example, or within Russia as part of an extremist nationalist movement - that would suggest a new era of terror attacks in Russia. Moscow's response, at this point, would be difficult to predict.
Regardless of where the bombing originated, Putin promised again on Wednesday that Russia's response would be unflinching. "It is necessary to fight mercilessly with terrorism and extremism," he said.
Thirty-five people were killed at the airport Monday when a suicide bomber or bombers detonated explosives in a reception area where drivers and others wait for incoming passengers on international flights. Between 110 and 125 people were hospitalized; government agencies continued to disagree on the exact number.
In assigning blame for the blast, Russian leaders on Tuesday drew a clear line between those responsible for security at the airport and those whose job it is to fight terrorism nationally.
President Dmitry Medvedev described airport security as "chaos," and officials launched a criminal investigation that could target Domodedovo's management. But after Medvedev met with leaders of the Federal Security Service (FSB), which is charged with preventing terrorism, he made no mention in his public remarks of the agency's inability to stop Monday's attack. Instead, he praised the agency's record.
One report on Tuesday said there were two bombers, a man and a woman, but others described a lone man. Sources told Russian wire agencies that the FSB had been on the lookout for a terrorist attack at an airport, but because it was expecting women to be the perpetrators, it missed the bomber.
"The FSB and law enforcement bodies have sufficient experience in such operations," Medvedev said. "We must act."
Putin is a veteran of the FSB and its predecessor, the KGB, and under him the agency has achieved unparalleled clout within the government. Critics say the agency has grown so powerful that it is beyond reproach and now beyond even the Kremlin's control.