Religious leaders have prayed for peace in Darfur outside Downing Street as part of an international day of action.
Protesters gathered outside the Sudanese embassy in London
The prime minister has written to every state in the EU to press for an end to violence in Darfur in western Sudan.
Tens of thousands of people have died and up to two million have been displaced in three years of conflict.
Pressure is mounting on Sudan to admit UN peacekeepers, with Foreign Secretary Margaret Beckett preparing for a week of talks at the UN in New York.
Mr Blair's letter coincides with a Darfur Day of Action in 30 cities worldwide.
Cardinal Cormac Murphy O'Connor, leader of the Catholic Church in England and Wales, was among the leaders from the Christian, Muslim and Jewish faiths at the event in London.
He said: "The situation is catastrophic in terms of the violence, the murders, the displacement of people."
A prayer from Archbishop Desmond Tutu - written with the other religious leaders - remembered not only the victims but the perpetrators.
"We pray that those who causing misery and death in Darfur will turn away from racism and violence - may they be forgiven when they turn to You instead."
They were met by Baroness Amos, Leader of the House of Lords, who said the world must not once again turn a blind eye to an unfolding crisis in Africa.
The Darfur Peace Agreement, signed by the government and one of the major rebel groups in May, has failed to end fighting between rival rebel factions.
The Sudanese government is resisting the continued presence of an African Union force in the region and a handover to United Nations peacekeepers.
Mr Blair said the EU should play a "central role" in peace efforts and that the Sudanese government should prepare to face isolation if it failed to respond to diplomatic pressure to end the "slaughter".
"We should strongly call upon the government of Sudan and non-signatories alike to stop immediately the violence in northern Darfur," he wrote in the letter, which has also been sent to European Commission president Jose Manuel Barroso.
Ms Beckett told the BBC: "The thing that would be... catastrophic would be to have a security vacuum where the African Union mission left and there was no-one to replace them."
Baroness Amos, the Leader of the House of Lords, said that if necessary, the British government would press for further sanctions and for human rights abuses to be investigated by the international criminal court.
"They have a responsibility to look after all of their citizens. We want that UN peacekeeping force in there. We can't see the kind of scale of devastation, human rights abuses, people being killed. The world community cannot stand back and watch this unfold yet again."
Up to two million people have been displaced in three years of conflict
But Sudan's junior foreign minister, Ali Khati, said the situation on the ground was improving. He denied that his government had bombed villages.
And he was critical of the Western media's coverage of events in Sudan.
"People there in the West, in Europe and the United States, are moved by the media. And the media is unfortunately moved by political agendas, and by people making problems in the Third World, like Sudan."
The crisis began in 2003 when ethnic African tribes revolted against the Arab-led Khartoum government.