International agencies say hundreds of civilians have been killed in the fighting and a quarter of a million more are trapped. They say further convoys must be permitted.
Sri Lanka's defence secretary, Gotabaya Rajapakse, told the BBC that the numbers are exaggerated, there are no civilian casualties and aid agencies are panicking.
Deaths
A UN convoy, which was trapped in the town of Puthukkudiyiruppu, succeeded in its second attempt in three days to evacuated the critically wounded civilians.
UN spokesman Gordon Weiss said the convoy had taken hundreds of civilians wounded by the fighting, including 50 critically wounded children, to hospital in Vavuniya.
UN spokesman: We saw 'dozens of people' killed
Mr Weiss said that other civilians were waiting to be evacuated but he was unclear exactly how many. He rejected the Sri Lankan government view that there was no humanitarian crisis in the north.
"Our staff witnessed the deaths and injuries of dozens of people over the weekend," he said.
"There are a quarter of a million who are imperilled because they have been forced into a pocket of territory about a third the size of London."
Later, the ICRC said that it had escorted 226 sick and wounded patients requiring urgent medical treatment from the north to Vavuniya Hospital.
Local journalists in the town are not being allowed to talk to anyone who has been evacuated from rebel-held areas.
The pro-rebel TamilNet website quoted a rebel spokesman, S Puleedevan, denying reports that the rebels had initially prevented the ICRC convoy from leaving.
INSURGENCY TIMELINE
1976: Liberation Tigers of Tamil Eelam form in the north-east
1987: India deploys peace-keepers to Tamil areas but they leave in 1990
2002: Government and rebels agree ceasefire
2006: Heavy fighting resumes
2009: Army takes main rebel bases of Kilinochchi and Mullaitivu
Mr Puleedevan described the reports as "mischievous".
"In fact, we have been repeatedly urging the ICRC to facilitate the unhindered transportation of injured civilians who need urgent attention and also for the provision of medical facilities locally," he said.
In the latest fighting, the army says that it has captured a key crossroads in the north.
Military spokesman Brig Udaya Nanayakkara said that troops had taken the Vishwamadu junction on Wednesday afternoon after heavy fighting.
The junction, near the village of Vishwamadu, lies along one of the few major roads remaining in rebel-held territory.
'No ceasefire'
The BBC's Ethirajan Anbarasan - who was taken by the army to a town just north of the former rebel administrative centre at Kilinochchi - said he passed abandoned fields and villages on his way to the war zone.
Our correspondent says senior army officials there say they have inflicted heavy damage on the Tigers. They also say they have captured one of the rebels' boat yards in which they found a small submarine and two unfinished submarines.
The defence ministry also said that the three "suicide boats" and a large haul of rebel maritime equipment were also discovered. There has been no independent confirmation of the claims and no word from the rebels.
The military has released pictures of captured rebel submarines
Both Amnesty International and Human Rights Watch (HRW) have expressed concern over the plight of civilians and have blamed both the government and the rebels.
On Wednesday Defence Secretary Gotabaya Rajapakse denied that the fighting had led to a humanitarian crisis in the north.
He also ruled out any ceasefire for humanitarian reasons, saying it would give the Tigers a chance to reorganise.
"The purpose of this offensive is to eradicate them," he said.
The military say they are involved in a final push against the retreating rebels.
Moving north from the captured rebel town of Mullaitivu, they are trying to secure the north-east coastline to encircle the rebels and say they hope to control the entire north within weeks.
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