The Russian leader, who cancelled two foreign visits after the incident, left no doubt as to his mood over this latest strike.
|Seek and destroy: Russian troops|
are under orders to hunt down
Chechen resistance groups
He said: "They must be dug up out of their basements and caves where they are still hiding and destroyed.
"Their main goal is to break up the political process" said Putin who believes Russian-imposed elections in the region will lead to an end to the Chechen war.
However, he ruled out an immediate end to Russia's military presence in the war-torn region, and said that strikes on Chechnya must be "well chosen," according to the Russian newspaper, Novosti.
Putin blamed Chechen separatists for the explosions at the weekend rock concert in Moscow in which 13 festival-goers died.
In a political process aimed at conveying the impression that Russia's counter-insurgency campaign in the republic has been won, the Russian president has named 5 October as the date for presidential elections in Chechnya.
The number of Chechens at the end of the Soviet era was estimated at 957,000 in a 1989 census.
But after two wars, a huge Russian military presence and the prevention of international organizations from working in the province - the number of Chechens was estimated at 800,000 in 1998 by the United Nations.
Additionally, 380,000 people are also reported to have left Chechnya as refugees, and more than 200,000 are internally displaced.
The number of Russian troops in the region is put at a quarter of the total remaining Chechen population by a human rights’ group, Amnesty International.
"Human rights abuses continue to take place on a daily basis in Chechnya," says the watchdog's June report.
"The UN Commission's lack of action on this situation is a blatant disregard of the suffering of the victims of such abuses and their relatives, and the risks to which civilians continue to be exposed," it added.
Amnesty claims that Chechen civilians continue to "disappear" during raids by Russian troops on villages, many have later been found in mass graves.
The organisation also stresses its disappointment with the UN Commission for Human Rights in choosing to remain silent for the second year, claiming violations of human rights and humanitarian law in Chechnya are well-documented.