(CNN) -- Sri Lankan officials rejected a proposed cease-fire from the Tamil Tiger rebels Sunday, warning instead that government troops intended to continue a new offensive until the group surrenders, a senior government official said.

Tamil demonstrators call for a cease-fire in Sri Lanka during a rally Saturday in Paris, France.

"The government is firm that (the rebels) lay down their arms and surrender. We do not recognize this so-called offer," said Lakshman Hulugalle, director of Sri Lanka's Media Center for National Security.

The proposed cease-fire came six days after the Sri Lankan army launched a new offensive against the Liberation Tigers of Tamil Elam (LTTE) in the country's northern area. Government troops made significant advances into rebel-held territory on Friday and Saturday, according to Sri Lankan Army sources.

A government-imposed deadline for the Tigers to surrender passed last Tuesday. Tens of thousands of displaced civilians currently remain wedged in a dwindling swath of territory controlled by the Tigers along the country's northeastern coast.

Government troops say they have rescued 39,000 civilians trapped in the area, but a U.N. refugee agency said Friday that a wave of "fresh displacement" has now exceeded 100,000 individuals.

"In the face of an unprecedented humanitarian crisis and in response to the calls made by the U.N., EU, the governments of the USA, India and others, the (LTTE) has announced an unilateral cease-fire. All of LTTE's offensive military operations will cease with immediate effect," the rebel leaders said in a written statement issued earlier Sunday.

"We welcome the attempts by the U.N. and its agencies to assist the civilian population and are ready to engage and cooperate with them to address the humanitarian needs of the population. ... We are in full agreement that the humanitarian crisis can only be overcome by declaration of an immediate cease-fire."

The Tiger leadership asked the international community to "pressure the Sri Lankan government to reciprocate" on the cease-fire offer.

The Tigers have been fighting for an independent state in Sri Lanka's northeast since 1983. As many as 70,000 people have been killed since the civil war began, and the group has been declared a terrorist organization by 32 countries, including the United States and the European Union.

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