"The ceasefire is purely for humanitarian purposes and the duration will depend on the response of the Sri Lankan government," Puleethevan told AFP by telephone from the last patch of rebel-held territory.
Rajapakse, who leads the government's military campaign against the Tigers, said there was no need for a ceasefire as the military was about to defeat the separatist fighters.
"It must be a joke," Rajapakse told AFP in response to the Tigers' ceasefire, which the rebels said would allow international aid agencies into the conflict zone to help civilians.
"What is the need for a ceasefire when they are running away? They should first lay down arms, surrender and let the people go," Rajapakse said.
The Liberation Tigers of Tamil Eelam (LTTE) said its ceasefire was "in the face of an unprecedented humanitarian crisis" and in response to international calls for a halt in fighting to allow help to reach trapped civilians.
"All of LTTE’s offensive military operations will cease