Official results in the first round of the presidential election in March showed Tsvangirai had won, but he did not have the outright majority required to avoid a run-off.
Since then the MDC, along with human-rights groups and Western governments, have accused Mugabe and his Zanu-PF party of organising a campaign of violence aimed at intimidating opposition supporters.
Mugabe, who is facing the most serious challenge to his 28-year rule at the June 27 election, blames the opposition for the violence.
On Wednesday, Ban Ki-moon, the UN secretary-general, voiced "profound alarm" at the situation in Zimbabwe saying that the violence, intimidation and arrests of opposition leaders could not lead to credible elections.
"Should these conditions continue to prevail, the legitimacy of the election outcomes would be in question," Ban told an informal session of the General Assembly.
Raila Odinga, the Kenyan prime minister, has called for an international peacekeeping force to be sent to Zimbabwe to ensure a free and fair election.
"What we need in Zimbabwe is actually an international peacekeeping force so that ... proper elections can be held," he said.
"Zimbabwe remains an eyesore on the African continent
"It's a big embarrassment that a leader can say on the eve of elections that he's not willing to hand over power" to an opponent, Odinga said in Washington.
Gordon Brown, the British prime minister, added to the growing number of leaders calling for increased monitoring of the poll.
"We have asked the regime to allow in observers for the 9,400 polling stations that exist," he told parliament on Wednesday.
"Hundreds of observers have gone in, more observers are to go in.
"We demand that these observers come from different parts of the world and not just from Africa."
Zimbabwe is allowing SADC to send a 400-strong observer mission to monitor the polls.