Also Tuesday, suspected rebels opened fire at an army post, injuring one soldier, said military spokesman Brig. Daya Ratnayake. The attack took place in Sri Lanka's northeastern port of Trincomalee, and the soldier's injuries were not life-threatening, he said.
The warning came after the rebels and two civilians were killed by unidentified assailants on Sunday in Trincomalee -- a town controlled by the government with pockets around it held by the rebels.
"We cannot exercise patience while our cadres and civilians are being killed, maimed and threatened by the military intelligence wing in the military-controlled areas," S.P. Thamilselvan, the rebel's political head, said in a letter to Hagrup Haukland, the cease-fire monitoring chief.
"Such attacks, continuing to take place in the current confused climate, are a serious threat to the stability of the cease-fire agreement," he said. "It appears to us that the government and its forces are taking actions to break the cease-fire agreement and to force a war on our nation."
The military has denied any responsibility for the killings.
"These accusations are completely unfounded," Ratnayake said, "We have no involvement whatsoever."
He said the attacks could be linked to factional fighting since a March 2004 split in the rebel group.
"The situation is serious and undermines the entire peace process," cease-fire monitoring chief Haukland said, adding that the escalating violence was "worrying."
Meanwhile, schools, shops and offices were closed and transport interrupted in Trincomalee on Tuesday to protest Sunday's killings.
"Tires were burned in a few places and we have moved to remove some road barriers," said local police chief Rohan Abeywardene.
Separately, suspected rebels lobbed a grenade at a police jeep near Trincomalee but it missed the target and exploded without causing any casualties, Abeywardene said.
The Tamil Tiger rebels waged a two-decade war for a separate state for Sri Lanka's ethnic minority Tamils until the cease-fire halted the conflict in 2002. Peace talks started after the truce, but have been deadlocked over rebel demands for wide-ranging autonomy.