Formed in 1975, the group has vowed to carve out a separate Tamil state in Sri Lanka.
Jacques de Maio, the head of Red Cross operations for South Asia, said: “People are being caught in the crossfire, hospitals and ambulances have been hit by shelling and several aid workers have been injured while evacuating the wounded.
“It’s high time to take decisive action and stop further bloodshed because time is running out.
“We don’t use indirect fire unless we are 100 per cent certain that those are LTTE camps or bases … This is all LTTE propaganda”
The Red Cross has appealed to both sides to allow civilians to leave the combat zone.
Sri Lanka’s military said the LTTE, who are fighting for the creation of an independent Tamil state in northern Sri Lanka, wanted to create a “last-minute civilian tragedy” because the army was about to completely defeat them.
Udaya Nanayakkara, a military spokesman, said claims of civilian deaths were part of a “cheap propaganda exercise” by the LTTE.
Pranab Mukherjee, India’s foreign minister, on a surprise visit to Sri Lanka on Tuesday, called for urgent measures to protect civilians caught up in the island’s ongoing fighting.
Sri Lanka’s minority ethnic Tamils have close cultural and religious links with the 55 million Tamil population in the south Indian state of Tamil Nadu.
Sri Lankan forces pushed into the northern village of Visuamadu, held by the LTTE, on Wednesday, a defence ministry official said.
The ministry claimed that Tamil separatists retreated their long-range artillery guns into an area declared a 35 square km “safe zone” for civilians, and were firing at the military from there.
Tony Birtley, Al Jazeera’s correspondent who visited the district of Mullaitivu under the oversight of the army, said that the LTTE appeared to have fled the town.
He said the town was largely empty, with most civilian residents apparently retreating with the Tamil Tigers.
The government has said civilians are being forced to move with the Tigers to act as human shields, but there has been no independent confirmation that is the case.
The Red Cross’ De Maio said: “When the dust settles, we may see countless victims and a terrible humanitarian situation unless civilians are protected and international humanitarian law is respected in all circumstances.”
The United Nations has issued similar warnings, with Ban Ki-moon, the UN secretary general, saying he was “deeply concerned” for the safety of civilians caught in the fighting.
In an interview with Al Jazeera, Gotabaya Rajapaksa, the Sri Lankan defence minister, said that government forces exercised extreme caution during the offensive and only fired on Tamil Tiger rebels.
The official death toll is unknown as medical officials have said they have been ordered by the health ministry in Colombo not to reveal casualty figures.
A fresh offensive against the Liberation Tigers of Tamil Eelam (LTTE) was launched by the government late last year, shrinking the northern territory under LTTE control, since heightened operations against the separatists began in mid-2007.
The military seized Mullaittivu on Sunday, which they claim was the LTTE’s last urban centre.