Mr Tsvangirai has taken refuge in the Dutch embassy, fearing for his safety
UN Secretary General Ban Ki-moon has said Zimbabwe's presidential run-off poll should be postponed following the withdrawal of the opposition candidate.
Mr Ban said Morgan Tsvangirai's decision was understandable, and condemned what he called a government campaign of violence and intimidation.
Later, the UN Security Council declared that it would be "impossible" to hold free and fair elections.
Zimbabwe election officials had said Friday's second round would go ahead.
Mr Tsvangirai has taken refuge in the Dutch embassy in the capital Harare.
A Dutch foreign ministry spokesman said Mr Tsvangirai feared for his safety, but had not requested asylum.
Zimbabwe's head of police, however, said Mr Tsvangirai was not in any danger.
On Monday, more than 60 supporters of Mr Tsvangirai's Movement for Democratic Change (MDC) party were arrested at its Harare headquarters.
'Too much violence'
The UN Security Council unanimously adopted a statement condemning the violence and saying that free and fair elections would be impossible to hold on 27 June.
UN chief says he is "distressed" by the situation in Zimbabwe
The non-binding statement is much watered down from a draft version circulated by Western countries on the council. But for the first time, Zimbabwe is criticised by South Africa, Russia and China.
Earlier, Mr Ban said that if the run-off took place as scheduled, it would only "deepen divisions within the country and produce a result that cannot be credible".
He said: "Conditions do not exist for free and fair elections right now in Zimbabwe. "There has been too much violence, too much intimidation."
He said the world had witnessed "fear, hostility and blatant attacks" against Zimbabwe's people.
Mr Mugabe and his Zanu-PF blame the opposition for the election violence
After discussing the issues with a number of African leaders, he said he strongly advised President Robert Mugabe's leadership to postpone the election until the right conditions were in place for people to vote freely and fairly.
Mr Ban added that what happened in Zimbabwe had significance beyond its borders and was the "single greatest challenge to regional stability".
The MDC won the parliamentary vote in March, and claims to have won the first round of the presidential contest outright. According to official results, Mr Tsvangirai led but failed to gain enough votes to avoid a run-off.
The BBC's John Simpson in Harare says few people in Zimbabwe even know that Mr Tsvangirai has withdrawn from the race, because the country's official media mention him and the MDC as little as possible.
He adds that it is clear that on Friday, Mr Mugabe will be elected, by however large or small a majority, as the next president of Zimbabwe.
ZIMBABWE AND ITS NEIGHBOURS
Zimbabwe's opposition wants neighbouring countries to persuade
Robert Mugabe to step down. So how are relations changing?
South Africa's leader Thabo Mbeki remains the key mediator. He has not
criticised Mr Mugabe, despite pressure from the ruling ANC.
Zambian President Levy Mwanawasa called Zimbabwe a "regional
embarrassment", before suffering a stroke on 29 June.
Angola's President Jose Eduardo dos Santos is one of Robert Mugabe's closest allies. He has urged Mr Mugabe to end the violence.
Botswana said Zimbabwe's 27 June run-off vote was so flawed by violence
that it could not be considered legitimate.
Namibia is an ally of Robert Mugabe. It wants to re-distribute white-owned farms to black villagers. It has not criticised the violence.
Mozambique has hosted some white farmers forced out of Zimbabwe when their land was seized. It is seen as sympathetic to the opposition.
Tanzania's ruling party has a history of backing Robert Mugabe's
Zanu-PF party. Its foreign minister has condemned the violence.
DR Congo's President Joseph Kabila is an ally of Robert Mugabe who
sent troops to help his father, Laurent Kabila, fight rebels.
Malawi is seen as neutral. But 3m people from Malawi are in Zimbabwe
and many were badly hit by the farm invasions.
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