In a statement on their website posted on Friday, the group also warned European cease-fire monitors that they travelled aboard Sri Lankan navy ships at their own risk.
The warning came after the Sri Lankan military said 17 sailors and 50 rebels had been killed in sea clashes off the coast of the north of the country – the worst military confrontation since a 2002 truce.
The Sri Lankan government responded to the attack by launching air strikes on rebel-held territory.
A flotilla of rebel boats attacked a navy troop transporter and combat boat on Thursday in what ceasefire monitors described as "gross violations" of the truce agreement and said the Tigers had no right to carry out operations at sea.
A monitor was aboard the transporter and the ship was flying the flag of the Sri Lanka Monitoring Mission (SLMM) when the rebels attacked.
"If you choose to ignore our warning and request, we are not responsible for the consequences"
The Tigers said they were entitled to carry out military exercises at sea and accused the navy of disturbing them.
"If (the) Sri Lankan navy disrupts our activities we will definitely retaliate," the statement said.
The Tigers also said that ceasefire monitors were protecting the navy by their presence.
"SLMM monitors are used by the Sri Lankan Navy as human shields," the rebel statement added.
"We urge you for the last time not to be on board Sri Lankan naval vessels until further notice from us.
"If you choose to ignore our warning and request, we are not responsible for the consequences.
"Please take this as the last warning to you."
Bombings and sea clashes have killed about 270 people in the past month, making it one of the bloodiest since the 2002 truce agreement.
The Tigers, who are fighting for a separate homeland for ethnic Tamils in the north and east, have withdrawn from peace talks indefinitely and said on Tuesday that Sri Lanka was moving towards the "fringes" of war.
Tamil Tigers website
Sri Lanka Monitoring Mission