Umarov's statement in a video posted late Monday was likely to add to jitters in Russia's capital and increase pressure on the government. Prime Minister Vladimir Putin, whose popularity has hinged on his tough line against the insurgency, recently admitted that Russia needs to learn from foreign experience in fighting terror.
The Jan. 24 bombing of Domodedovo Airport killed 36 people and injured about 180. Russian investigators said the bomber was a 20-year-old man from the Caucasus region that includes Chechnya, but have not released his name or other details.
Top security officials briefed parliament Tuesday about the investigation in a closed session. Vladimir Vasilyev, the head of parliament's security committee, told reporters after the session that at least two people have been arrested on suspicion of involvement in the bombing. The arrests appeared to be related to last week's announcement that several people suspected of having information about the bombing had been detained.
Vasilyev and other lawmakers said the security officials identified the bomber and his accomplices but ordered their names withheld from the public.
"All residents of our country need to realize that we will have to live under the threat of terror for a long time to come," Vasilyev said.
His deputy, Gennady Gudkov, said an autonomous group of several militants had carried out the attack, but added that Umarov could have links to the attack. Gudkov said that rebels operate in separate cells, which makes it harder to track them down.
Umarov has claimed responsibility for an array of terrorist attacks, including last year's double suicide bombing of the Moscow subway system that killed 40 people. He is seen more as an ideological than a military figure, as many terrorist cells operate autonomously and shun centralized command.
The Chechen warlord said he ordered the airport bombing and that many more "special operations" will follow, if Russia does not allow the Caucasus to become an independent Islamic state governed by sharia law.
"Among us there are hundreds of brothers who are prepared to sacrifice themselves" in further attacks, Umarov said in the video posted on a website affiliated with Islamic rebels in the Caucasus.
"We can at any time carry out operations where we want," he said, clad in fatigues and wearing a black skullcap.
Over the weekend, the Kavkaz Center website released another video in which Umarov appeared with a young man whom he said was being sent to Moscow on a suicide mission. No mention was made of the airport bombing, and it was unclear when the video was made.
Chechen rebels have fought two full-scale wars against Russian forces since 1994. Major offensives in the second war died down about a decade ago, but the Islamic insurgency has spread across neighboring North Caucasus provinces, stoked by poverty, official corruption and security force abuses against civilians.
The Islamic militancy that once focused on Chechnya's independence has taken on the broader goal of creating an Islamic state across the entire North Caucasus region. While attacks in Chechnya have become rarer under the brutal rule of a Moscow-backed regional strongman, Ramzan Kadyrov, attacks on police and officials in neighboring provinces happen almost daily.
Putin said last week that foreign special services are often more efficient in dealing with the terror threat and that there is a need to learn from their experience. He also acknowledged that high unemployment in the North Caucasus creates a breeding ground for terrorism.
Following the airport bombing, President Dmitry Medvedev fired several top transport police officials and ordered heightened security measures at all the country's main transport hubs, including major railway stations. Putin also dismissed the head of a federal agency overseeing transport security, his office said Tuesday.
The Federal Security Service, or FSB, said Tuesday that two officers had been fired and several others were reprimanded over the bombing. The announcement came after Gudkov told reporters that as many as 10 FSB officers had lost their jobs.
Moscow has seen a rash of bomb threats since the airport bombing, including some that have forced the evacuations of shopping centers and train stations, but no explosives have been found.
AP writer Jim Heintz contributed to this report.