The UN, like all international organisations and journalists, is banned from the war zone by the government.
However, Weiss said he was confident that the report of the deaths and more than 1,000 others wounded from a doctor working at a makeshift state-hospital in the area were correct.
"[Ban Ki-moon], the UN secretary-general, has consistently asked that we be allowed into the area to assess for ourselves the true condition of people there ... we are relying on the only sources we have," Weiss said.
"The government doctors reporting from that zone, to the best of our knowledge, have proved consistently reliable."
A UN statement said Ban Ki-moon was "appalled" at the deaths of civilians and deeply concerned by the continued use of heavy weapons in the conflict.
"The LTTE must immediately allow the remaining civilians in the conflict zone to leave," Ban said, adding that Colombo must "explore all possible options" to end the fighting.
Each side should remember the world will not accept further violations of international law, he said.
The US also voiced concern on Monday about what it called an "unacceptably high" level of civilian casualties.
"We have repeatedly urged the Tamil Tigers to lay down its arms and allow the civilians to leave," Ian Kelly, a state department spokesman, said.
"The government of Sri Lanka should abide by its April 27th statement that combat operations have concluded and security forces should end the use of heavy weapons which of course could cause civilian casualties."
Thileepan Parthipan, an LTTE spokesman, blamed the government for the deaths.
"In that area, there has been continuous shelling. Many Tamil civilians were killed," he said.
"More than 3,500 people were injured. A nearby hospital received 378 dead bodies.
"Some bodies are still on the streets. There were people inside bunkers which collapsed in the shelling."
Anton Stephan, a Catholic priest inside the zone, also spoke of heavy military bombardment.
"They are fighting civilians. They're using cluster bombs, cannons. They're shooting towards people," he said.
However, the government accused the LTTE of killing civilians in order to blame the deaths on the military.
Gotobaya Rajapaksa, Sri Lanka's defence secretary, told Al Jazeera on Monday that the government is not to blame for the civilian deaths "at all".
"It is very easy to find out who is killing the civilians because there are 200,000 people who have escaped from the LTTE area to government-controlled areas and anybody can talk to these people," he said.
"The day before yesterday, a thousand people tried to cross to a government-controlled area and the LTTE fired directly at these people."
The government announced on Friday new borders for the region it calls a civilian safety zone in the northeast where the fighting is happening. The coastal area is now 3sq km in size.
The UN called for fighting to halt and for the government to help civilians.
|Tens of thousands of civilians have fled the northeastern war zone in recent weeks [AFP]
"The UN has repeatedly said to the government that they must not use aerial attacks and heavy ordnance in a tiny patch of land that is about the size of Central Park in New York and we have also said to the LTTE that they need to separate their forces from the civilians who are trapped in this area," Weiss said.
"There are about 50,000 to 100,000 civilians in this area and they need to let these civilians escape from this zone."
Paul Castella, the head of International Committee of the Red Cross in Sri Lanka, told Al Jazeera that those trapped "have very little to eat, almost no medicines and very little way to protect themselves from the sun.
"In practice, at any time of the day or night, people can be hit by a shell or a stray bullet. And this is making life for the people extremely difficult."
'Very difficult position'
Weiss aqcknowledged that the Sri Lankan government was in "a very difficult position" regarding civilians' safety.
"They are well within their rights to be taking the Tamil Tigers head on. The Tamil Tigers have proven themselves to be a brutal and intractable foe, and they are responsible for keeping civilians inside this zone.
"The onus is really principally on the government at this stage because they are the sovereign government of this territory"
"But that being said, the onus is really principally on the government at this stage because they are the sovereign government of this territory. They have a higher degree of responsibility.
"They are signed up to international treaties and protocols that protect civilians in precisely these circumstances and that's why international humanitarian law and the wars law exist."
The LTTE is believed to be close to defeat in its 26-year battle for a separate homeland in the northeast of the island for the country's minority Tamils.
The group used to control a wide swath of Sri Lanka's north, but the territory they hold has been reduced to the 3km strip of coastline following military advances this year.
In recent weeks fierce fighting has forced tens of thousands of civilians to flee to state-run refugee camps outside the zone, but more remain trapped by the conflict.
The government has refused to continence a humanitarian ceasefire saying it would allow the LTTE to regroup.