Each side should remember that the world will not accept further violations of international law, Ban said.
The US has also voiced concern about what it called an "unacceptably high" level of civilian casualties in the shelling over the weekend.
"We have repeatedly urged the Tamil Tigers to lay down its arms and allow the civilians to leave," Ian Kelly, a US 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."
UN officials in Sri Lanka described the shelling as a "bloodbath".
"We have consistently warned of a bloodbath scenario, and the large-scale killing of civilians over the weekend, including at least more than 100 children, shows that that bloodbath has now become a reality," Gordon Weiss, the UN spokesman for Sri Lanka, told Al Jazeera on Monday.
The LTTE and the government have blamed each other for the deaths of the civilians.
'War without witness'
David Miliband, Britain's foreign secretary, called for all levels of the UN to hold discussions on the conditions facing Sri Lankan civilians trapped by the conflict.
"No one can be in any doubt that this is an issue that deserves the international community's attention," he said at UN headquarters in New York.
|Tens of thousands of civilians have fled the northeastern war zone in recent weeks [AFP]
"The civilians ... trapped in the zone - up to 50,000 in an area of just three sq km - are the victims of what at the moment is a war without witness."
The Sri Lankan government announced on Friday, new borders for the region it describes as a civilian safety zone.
The UN called for the fighting to be halted and for the government to help civilians.
In recent weeks, fierce fighting has forced tens of thousands of civilians to flee to state-run refugee camps outside the zone, but many more remain trapped by the conflict.
The LTTE is believed to be close to defeat in its 26-year battle for a separate homeland in the north and east of the island for the country's minority Tamils.
The government has refused to declare a humanitarian ceasefire saying it would allow the LTTE to regroup.