"The Sinhala nation is trying to destroy the Tamil nation," the LTTE chief said in the speech, a text of which was distributed by the Tigers.
"It is unleashing unthinkable violence against another people. It only desires to find a solution to the Tamil question through military might and oppression."
Claim and denial
Prabhakaran's speech coincided with a fresh exchange of accusations between his group and the government.
The LTTE said 13 civilians were killed by a military mine in Killinochchi, a rebel-controlled area, on Tuesday, but the government said the air force had bombed an LTTE radio station in the north.
The military denied any attack on civilians in Kilinochchi but acknowledged that it bombed the radio station hours before Prabhakaran's speech.
It was not immediately clear if this prevented the speech from being broadcast across the north, but the full transcript was made available via an LTTE website.
The Tigers blamed the air raids for the deaths of five radio-station employees and four others, including a 14-year-old girl.
They said the civilians were participating in the Tigers "Heroes' Week" celebrations when the military unit exploded the claymore fragmentation mine.
The Tigers themselves often use such mines against government forces.
In his speech, Prabhakaran said the current government "is never going to realise that the Tamil national question cannot be resolved by military oppression.
"All the Sinhala political parties are essentially chauvinistic and anti-Tamil. To expect a political solution from any of these southern parties is political naivety," he said.
Prabhakaran's comments underscored that the Tigers, who lost their chief negotiator in a government bombing raid in November, are no longer interested in dealing with Norwegian peace brokers overseeing a faltering 2002 truce.
Prabhakaran, who turned 53 on Monday, said the Nordic peace watchdog had in any case "covered its eyes, tied its hands behind its back and went to sleep in Colombo".
The LTTE was ejected from the east in July, and the government has said it has sunk the bulk of the rebels' fabled fleet of ships in a string of naval clashes.
But Prabhakaran said Colombo was "overconfident of its military victory" in the east and that successive Sri Lankan governments have "always misunderstood our freedom struggle [and] consistently underestimated us".
"The Sinhala military has fallen yet again into the net we spread and it is now forced to commit large numbers of troops to rule land without people," Prabhakaran said.
"Caught in a territorial trap, it will soon be forced to face the serious consequences of its misguided ambitions.
"Thousands of our fighters are standing ready to fight with determination for our just goal of freedom and we will overcome the hurdles before us and liberate our motherland."
On Monday, Gotabhaya Rajapakse, the country's defence secretary, said that his forces were now going all out to kill Prabhakaran and recapture the north.