SP Thamilselvan, the armed separitist group's political leader, said in a letter to the Norwegian peace envoy, Jon Hanssen-Bauer, on Saturday that unless the military halted its actions, the Tigers would not attend talks.
Thamilselvan said: "We [Tamil Tigers] will be forced into an unfortunate situation where we will have to re-examine our decision [to hold talks]."
The Sri Lankan government says it reserves the right to retaliate if the Tigers attack security forces.
The army was five kilometres inside Tiger territory in the eastern district of Batticaloa early on Saturday, after the pushing through Tiger frontlines on Friday, officials said.
The latest military attacks have been condemned by truce monitors and aid workers in Sri Lanka.
The military said the Tigers had destroyed a bridge north of Batticaloa as security forces advanced towards a village called Ponichchankeni.
"Our troops pushed past the rebel forward defence line as far as Ponichchankeni," a military spokesperson said. "There is artillery and mortar fire on and off."
The Tigers said that a three-pronged attack by the army to push past Ponichchankeni had been thwarted.
S Elilam, leader of the separatists' political wing in the east, said on the website tamilnet (www.tamilnet.com): "This offensive demonstrated that Colombo was not sincere in proceeding with talks."
A further three miles north, international aid agencies had already pulled staff out of the town of Vakarai because of security fears.
The town is sheltering thousands of displaced civilians.
Military officers have said they are keen to inflict as many casualties on the rebels as possible before talks, which are due to be held in Geneva on October 28 and 29.