Sri Lanka's president, Mahinda Rajapaksa, today gave the Tamil Tigers 48 hours to allow civilians to leave an area of dense jungle in which the rebels are mounting a last stand, but the government refused to grant a ceasefire, declaring its intention to eradicate the guerilla force after more than three decades of conflict.

Humanitarian agencies voiced concern over the fate of an estimated 250,000 Tamil civilians trapped by the fighting, and said that hundreds had already been killed. The Red Cross was today negotiating with the Liberation Tigers of Tamil Eelam (LTTE), as the rebels are formally known, to coordinate the transfer of civilians cornered in the 300 square kilometres of jungle and scattered villages still controlled by the Tigers.

Since the beginning of the year, the rebels have lost every town they once controlled, including their de facto capital, Kilinochchi, their main coastal town, Mullaittivu, and the strategically vital Elephant Pass.

The government began its offensive after walking out of a six-year-old Norwegian-brokered ceasefire, which had been violated repeatedly. The Sri Lankan army has nearly doubled in size over recent years and has new weapons bought from China and Pakistan, coupled with new training and special forces training, reported to have come from the US and India.

The Tigers' supply routes and possible means of escape have been cut off by joint patrols by the Sri Lankan and Indian navies, and the whereabouts of the Tigers' leader, Velupillai Prabhakaran, are unknown.

As it closes in on the surviving Tigers, the Colombo government appears determined not to give them pause to regroup, and has said the number of civilian casualties has been exaggerated.

The human rights and disaster management minister, Mahinda Samarasinghe, said: "We are determined not to have a ceasefire, and we are determined to eradicate terrorism in Sri Lanka."

Today, President Rajapaksa called on the Tigers to help spare the lives of civilians. "I urge the LTTE, within the next 48 hours, to allow free movement of civilians to ensure their safety and security. For all those civilians, I assure a safe passage to a secure environment," he said in an appeal posted on a government website.

A spokesman at the Sri Lankan high commission said that although the army would not declare a total ceasefire, it was taking care not to direct fire at areas where civilians were known to have congregated.

However, a Tamil Tiger spokesman, Balasingham Nadesan, said today that the government had increased artillery attacks on civilian areas.

The conflicting claims could not be independently confirmed as the Sri Lankan government was blocking reporters and all humanitarian groups except the Red Cross from approaching the conflict zone. The independent group Reporters Without Borders said the ban was "deplorable".

The UN high commissioner for human rights, Navi Pillay expressed "serious alarm" over the fate of civilians in the north.

"It seems there may have been very grave breaches of human rights by both sides in the conflict, and it is imperative that we find out more about what exactly has been going on," Pillay said.

The International Committee of the Red Cross has said that the situation in the north-east "remains precarious for thousands".

Britain announced a doubling in its humanitarian aid budget for the war zone, with an extra £2.5m for Red Cross operations and relief convoys. The international development secretary, Douglas Alexander, said he welcomed President Rajapaksa's offer of safe passage but added: "I urge all parties to make sure that this safe passage is implemented and that efforts are made to assist civilians to move away from danger."

The government wants the civilians moved to "model villages" – specially built camps that can be policed and isolated from the Tigers. Aid agencies have been reluctant to fund such schemes, pressing instead for the displaced population to return as soon as safe and feasible to their home villages.

Observers said a meaningful ceasefire was unlikely while the government felt so close to eliminating the LTTE as a force for the first time since its formation in 1976, in response to perceived discrimination by the majority Sinhalese government against ethnic Tamils.

"In the bigger scheme of things, the Tigers seem very badly damaged, and quite likely mortally wounded as a fighting force that holds territory," Alan Keenan, an Sri Lankan-based analyst for the International Crisis Group, said last night. "The question now is to what extent they retain the capacity to fight a guerilla war and carry out an low-level or medium level insurgency."

Keenan said the conflict was unlikely to end without a political solution, which would require both the government and the Tigers allowing independent political parties to emerge representing the views and interests of ordinary Tamils.