The minister brushed aside international pleas for a diplomatic solution and said President Boris Yeltsin, who has broken off a holiday to return to Moscow, fully supported the operation to finish the job Russian forces failed to do in the 1994-1996 Chechen war.
Marshal Sergeyev's pledge to fight to the finish this time expands the Russian invasion of Chechnya well beyond the limited intervention originally envisaged and raises the prospect of a bigger humanitarian disaster than feared.
Six weeks into the Russian offensive, an estimated 180,000 Chechen civilians have fled to neighbouring Ingushetia and are camped there in squalor, hunger and cold, with aid only from the Russian government. Around 170,000 more are inside Chechnya in freezing temperatures with no access to relief.
Thousands trying to flee are stopped by Russians at the border crossing at Kavkaz. Those who get through say there are many burnt-out cars on the road, hit by Russian aircraft.
But there is no sign of an international aid response. A UN mission flew to Ingushetia yesterday but its refugee and aid agencies remain constrained because the Russians view this as "an internal crisis" Moscow has to "invite" the UN in.
The big charities including Oxfam and Christian Aid are staying away because they say the risks of kidnapping and murder are too great. Of 15 British agencies whose fund-raising activities are co-ordinated by the London-based Disasters and Emergencies Committee, not one has sent assistance to Chechnya.
"We are very aware of the horror but we are not prepared to put our staff in a situation that we could not be sure was secure for them," said Adam Leach of Oxfam. "Our assessment is that neither Chechnya nor the surrounding areas are safe. Everyone's hands are tied by the same security problem."
The Red Cross is the only international humanitarian relief organisation active in the region and it has been forced to scale down programmes inside Chechnya because staff in the capital Grozny are under siege.
"There are very real concerns for health" said Lyndall Sachs of the UNHCR. "People do not have warm clothing or water. Children have no shoes. Diseases are breaking out. There are lice and many people have scabies. These conditions make Kosovo look mild."
The war is being driven by the political power play in Moscow. Russian success or failure in conquering Chechnya will determine the future of Vladimir Putin, the prime minister, who launched the war, and the outcome of the struggle in Moscow to succeed President Yeltsin in the election next year.
Artillery and aircraft continued to pound Chechnya yesterday as Russian forces advanced through the heavily populated towns and villages around Grozny. President Aslan Maskhadov, the Chechen leader, said yesterday 3,600 Chechens had died in the war.
Marshal Sergeyev said his soldiers have sealed off Gudermes, the second Chechen city. Russia is relying on massive use of firepower to keep down its casualties. The marshal said "no storming of Grozny will take place" and he was using "artillery and the air force to destroy the [Chechen] gangs and their camps."
President Maskhadov has 20,000 to 30,000 experienced guerrillas with light weapons. Russia has an estimated 100,000 troops.