Journalists flown to Kilinochchi were shown a large haul of mortars and small arms said to have been captured from the Tigers in recent battles.
Brigadier Silva said his unit had killed 5,953 Tiger fighters and wounded another 2,938 since September 2007, when a Norwegian-backed truce began to collapse.
He did not give corresponding military casualties.
The commander said a rebel spokesman who surrendered to government troops earlier in the week reported that Velupillai Prabhakaran, 54, was preparing to put up a final stand of his cornered and outnumbered separatist army.
The Tamil Tiger spokesman "says that Prabhakaran was living inside and that he will be there until the last moment," Brigadier Shavendra Silva told reporters.
"But, even at the last minute, he will try to escape," said the commander, who is spearheading the attack on the Liberation Tigers of Tamil Eelam (LTTE).
Silva told reporters flown to the former Tiger capital of Kilinochchi, 330 kilometres (180 miles) north