Tamils in the UK have been protesting outside Parliament for several weeks
The UK has told Sri Lanka it may face a potential war crimes probe over deaths of civilians in the island's conflict, a Foreign Office minister has said.
In a Commons debate, Bill Rammell said a UN estimate of 6,500 casualties since January was "shocking and appalling".
He said Britain backed an early inquiry into shelling by government forces fighting Tamil Tiger separatist rebels.
Labour MP Keith Vaz, chairman of the home affairs committee, appealed for UK intervention to stop the conflict.
The debate also heard demands for diplomatic relations be broken off with Sri Lanka.
It comes as the United Nations Security Council asked the Sri Lankan government and the Tamil Tigers to ensure the safety of civilians trapped in the conflict in the north-east.
The government in Colombo said it would not halt the offensive because it would give the rebels time to recover.
Hundreds of Tamil protesters have been occupying the square opposite Parliament for several weeks, urging the government to help secure a ceasefire.
Mr Rammell told the Commons the message from the UK government was that the "killing has to stop".
"The use of heavy weapons in an area of such intense civilian occupation will inevitably lead to civilian casualties, making it very difficult to comply with the requirements under international law to minimise civilian casualties," he said.
"We would support an early investigation into all incidents that may have resulted in civilian casualties, particularly the reported shelling of hospitals, to determine whether war crimes have been committed."
Labour's Andrew Dismore, chairman of Parliament's Committee on Human Rights, suggested it was "time the rest of the world turned their back on the Sri Lankan government, isolated them and held them to account".
In response to a question from Liberal Democrat foreign affairs spokesman Edward Davey, Mr Rammell said the government had made it "absolutely clear" to Sri Lanka that it supports an investigation on "any allegations of war crimes".
He added: "We have consistently maintained that both sides have to abide by their obligations under international humanitarian law and do everything possible to avoid putting civilians at unnecessary risk."
Tory spokesman Keith Simpson said he supported the government's efforts and raised concerns about the conditions in the conflict zone.
Mr Vaz said: "That so many people should be in such a small area attempting to live, let alone under fire, is absolutely horrific."
He said: "We intervened in Kosovo. I accepted the dossier that the then prime minister presented to the House. I voted to intervene in Iraq. I say we cannot stand aside."
Earlier this week, Foreign Secretary David Miliband and US Secretary of State Hillary Clinton urged all sides in Sri Lanka to end hostilities and allow for the safe evacuation of trapped civilians.
In a joint statement following talks in Washington, they called for "a political solution that reconciles all Sri Lankans, and establishes a meaningful role for Tamil and other minorities in national political life".