Speaking in an undated video posted on a Chechen rebel website this weekend, Umarov makes no direct reference to the Jan. 24 suicide bombing at Moscow's Domodedovo Airport, which killed 36 people and wounded 180.
No one has claimed responsibility for that attack, but suspicion has fallen on militants from the Caucasus region in Russia's south, which is gripped by an Islamic insurgency that appears to be intensifying.
Investigators said the bomber was a 20-year-old man from the Caucasus, but have not released his name.
Umarov said the man standing beside him in the shadowy video was a martyr being sent on a special operation aimed at "waking up" those who quietly accept the policies of Prime Minister Vladimir Putin.
"If that is not enough, then other blows will follow," the rebel leader said. "I am 100 percent confident in telling you that if it is the will of the Almighty, if the mercy of Allah will be with us, then we will make this year for you the year of blood and tears."
He said the attacks were retaliation for abuses committed in the Caucasus and also against people from the Caucasus living in Moscow and other Russian cities, where rising ethnic tensions have led to violent demonstrations and bloodshed in recent months.
Putin unleashed a second war on Chechnya in late 1999 to restore Kremlin control, and he has tolerated the brutal rule of Chechen leader Ramzan Kadyrov, who has brought an uneasy peace to the republic. The insurgency has since found more fertile ground in Dagestan, Ingushetia and other neighboring Muslim republics.
Umarov, who seeks to create a Caucasus emirate independent from Russia and governed by Shariah law, said he could call on 50 to 60 suicide bombers if necessary.
He was flanked on the video by the commander of a group said to train suicide bombers and by the young man, all three of them bearded and wearing fatigues.
The young man said he was ready to give his life for Allah and to "free our land from enemies."
The website KavkazCenter.com said it was unknown where or when Umarov filmed the video posted Saturday.