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.
Putin said Tuesday that "retribution is inevitable" for the attack. "I have no doubt that this crime will be resolved."
Both Putin and Medvedev have said these sorts of things after previous terrorist acts, even as the number of attacks in Russia, many of which attract little attention, has been increasing sharply.
Fears of a clampdown
Each major attack - the most recent before Monday's was on the Moscow Metro last March - brings a strengthening of central authority, said Ilya Yashin, the leader of the youth wing of Solidarity, an opposition party. "And yet we have bombs in the center of Russia," he said. "Not a single Russian has a feeling of security."
Yashin said he worries that the government might exploit the bombing by banning demonstrations, possibly revoking the Russian Constitution's Article 31, which, though rarely observed, guarantees freedom of assembly.
Vladimir Ryzhkov, another opposition leader and a former speaker of the State Duma, or lower house of parliament, said he doesn't expect further clampdowns on freedoms.
"Everything has been done," he said. "Governors are no longer elected but appointed. Mayors are barely elected. We don't have free Duma elections, we don't have free media, opposition parties cannot register or take part in elections.
"I can't imagine what more can be done."
The problem, he said, is that nothing will be done about terrorism, either. "There will be no real reaction, no reforms, no good changes. That means in the coming months we will have another attack."
It is not for a lack of manpower. The various police and security forces in Russia far outnumber the army. The police presence at demonstrations is always heavy.
But critics say the FSB and other agencies are not geared toward the prevention of terrorism. Their main function, said Andrei Soldatov, an investigative journalist, is to preserve the stability of the state. And an incident like the one at Domodedovo isn't seen as a threat to the state's foundation, he said.
Domodedovo was back to normal Tuesday afternoon. Flights were once again coming in from Munich, Berlin, Brussels, Hurghada, Odessa, Vienna, London and Frankfurt. One difference was noticeable: The metal detectors were operating, and everyone walked through them after entering the arrival hall.
A blue cordon channeled arriving passengers past a partitioned-off area, where sheets of blue and green plastic hung from the ceiling. The sounds of hammers and saws came from within, and a sign on the partition said, in English and Russian, "Sorry for the Inconvenience."
Incoming passengers filed through, many not noticing a large pile of flowers on the floor next to the partition. Red carnations were stacked high next to a dozen roses. Tea lights flickered in three large, translucent plastic drinking cups. One man crossed himself as he walked rapidly by.
"I'm here every day," said Eduard Mkhitaryan, one of the drivers lined up as usual along the blue cordon. Monday he was later than usual because the London flight was delayed. He arrived at 5 p.m., less than 30 minutes after the explosion. The police, he said, had not yet come.
"It was awful," he said, briefly recalling smoke, panic, blood. "It was frightening. I don't want to talk about it. I want to try to forget it."
Like others at the airport, Mkhitaryan said there was no use worrying about returning to the scene of the explosion. You have to work. Nothing will change. "If nothing changed after the Metro explosions, it won't change now," he said. "It's the mentality."
Another driver, Viktor Fakunin, said he wasn't afraid to show up at the airport Tuesday. "You have your destiny, and you cannot run away from it," he said. "If you are destined to hang, you will never drown."
Domodedovo is an easy target for presidential criticism. An ice storm in late December led to stupefying delays there, so its management was already under fire. The airport's directors and the Interior Ministry traded accusations Tuesday over who is responsible for security in the outer parts of the terminals.
"So Domodedovo is blamed not only for natural catastrophes, but also for terrorist acts," said Soldatov, the journalist. "Domodedovo is not responsible for the struggle against terrorism. But somebody needs to be blamed. Medvedev needs to present something to the people. He can't put pressure on the security services."
The security and especially the intelligence services should be blamed for failing to prevent the attack, said Gennady Gudkov, deputy head of the State Duma's security committee. But given the corruption in the government and the police, he said in a radio interview, terrorists will keep finding opportunities.