But Gotabaya Rajapaksa, the Sri Lanka defence secretary, said: "That is a joke.
"They were not fighting with us, they were running from us. There is no need of a ceasefire. They must surrender. That is it."
Brigadier Udaya Nanayakkara, a spokesman for the Sri Lankan military, told Al Jazeera: "We have very clearly indicated to them from the beginning that they have to lay down their arms and come and surrender.
"We expect all the LTTE cadres to come and surrender. It will automatically become a ceasefire if they lay down arms and surrender."
David Chater, Al Jazeera's correspondent in Colombo, said: "The [LTTE] announcement is just another weapon in a propaganda war.
"The government has said all along there would not be a pause in the fighting ... as the Tamil Tigers have previously used it to strengthen their positions and take child soldiers into their ranks.
"A unilateral ceasefire does actually put pressure on the Sri Lanka government as it means ... any pause would allow John Holmes, the top United Nations' humanitarian official, to go in and assess the situation."
Later, the government made a small concession to international pressure, agreeing to allow two UN representatives into the northern conflict zone.
Suren Surendiran, a Tamil activist and spokesman for the British Tamils Forum, told Al Jazeera: "What the Sri Lankan government is doing is a slow genocide.
"I expect the Sri Lankan government to cease all hostilities because the Sri Lankan government today have run 39 bombing sorties within the no-fire zone.
"Yesterday, they ran 25 bombing campaigns and 30 bombs were dropped and 174 people were killed - 48 of them were children. There is no food and there is no medicine."
Meanwhile, Balasingham Nadesan, the political head of the LTTE, told Al Jazeera that his group had the "confidence" to defeat the military.
"The Sri Lankan government is not interested in political solutions, they are always interested in military means to resolve the issue. That is impossible."
|Civilians remaining in the conflict zone are believed to be without sufficient food [AFP]
Nadesan also rejected accusations that LTTE fighters have used civilians as human shields.
"This is a fabricated allegation by the Sri Lankan government. We never use other people as human shields. We sacrifice our lives for our people, therefore we are like human shields for our people."
Sri Lanka's air force earlier denied claims that it had dropped bombs close to trapped civilians, after a Tamil television channel in Canada released a video appearing to show a Sri Lankan warplane shelling areas as civilians sheltered in trenches, saying the raids had been carried out over the past two days.
Janka Nayakkara, a Sri Lankan air force spokesman, told Al Jazeera: "These are just baseless allegations ... the air force has not carried out any offensive operations."
It is impossible to independently verify the veracity of the video footage as journalists and aid agencies are banned from entering the country's conflict zone.
The claims came as Holmes arrived in Sri Lanka for talks with the government on getting aid to people trapped in the conflict.
"The top priority remains the preservation of the lives of the tens of thousands of civilians still trapped inside the combat zone," Holmes said.
Gordon Weiss, the UN spokesman in Sri Lanka, told Al Jazeera that Holmes would press "top government officials" to allow UN teams and aid to reach trapped civilians.
"He will be taking to them the very clear message that has been repeated many times ... that civilians must not be made to suffer in the course of this conflict to the extent that they obviously are," he said.
The civilians' situation has deteriorated in recent days with the Sri Lankan military pressing ahead with its offensive to destroy the LTTE in a war that has been raging for a quarter of a century.
Aid workers say more than 100,000 civilians have packed into government-run camps for the displaced after managing to flee the conflict zone.
The Tigers, listed as a "terror group" by many Western nations, have been fighting since 1983 for an ethnic Tamil state in the north and east after decades of what they call marginalisation by governments dominated by the Sinhalese majority.