The results of the presidential election have not been released.
Mr Tsvangirai says he won outright but the ruling party has said no candidate gained 50% of the vote, so a run-off will be needed.
The opposition says its supporters are being attacked ahead of a possible run-off - claims denied by the government.
Earlier, the leaders of the Anglican church called for international action to prevent violence in Zimbabwe reaching "horrific levels".
Meanwhile, a Chinese foreign ministry official said a ship carrying weapons to Zimbabwe might return to China.
'Accept result'
Independent Zimbabwean monitors say Mr Tsvangirai gained 49% of the vote - just short of the threshold for outright victory - but more than President Mugabe.
The opposition Movement for Democratic Change (MDC) says its leader gained 50.3% and so should be declared the winner.
Zimbabwe's President Robert Mugabe has been under fire over March's disputed elections. His neighbours have been supportive but regional differences are now emerging.
There have been some suggestions that a government of national unity would be the best way of solving the impasse.
"We think in this situation we have a clear victor," said Ms Frazer, the senior US envoy to Africa.
"Morgan Tsvangirai won and perhaps outright, at which point you don't need a government of national unity. You have to accept the result."
But she said that any results released would not have any credibility and added that: "There may need to be a political solution, a negotiated solution."
This was a suggestion backed by Jacob Zuma, leader of South Africa's ANC.
"The two parties must be made to talk," he told the BBC.
Mr Tsvangirai has been in Mozambique, on the latest leg of his tour of African countries, trying to increase pressure on Mr Mugabe.
He is staying out of Zimbabwe, amid fears for his safety.
Archbishop of York John Sentamu said President Mugabe "is living on borrowed time".
Archbishop Sentamu, who is originally from Uganda, also urged police and soldiers not to be used for political ends - some reports suggest the security forces have led attacks on opposition supporters.
"I am saying to the police officers and the army people... you are not there to prop up a government, you are not there to be used as an arm of repression."
Ship 'recalled'
The opposition said the weapons on board the Chinese ship would be used against its supporters and that 10 had been killed so far.
This was denied by Zanu-PF spokesman Patrick Chinamasa. He said every country had the right to buy weapons.
The US has urged China to recall the ship - the An Yue Jiang, which was not allowed to unload in South Africa - before the cargo could be transported to landlocked Zimbabwe.
The British government has also called for an international arms embargo on Zimbabwe.
Zambia's president urged African countries not to let the arms, which reportedly include three million rounds of ammunition, 1,500 rocket-propelled grenades and 2,500 mortar rounds, pass through their territories.
Chinese foreign ministry spokeswoman Jiang Yu condemned the US intervention but said she thought the ship would return, as it has not been able to dock.
"To my knowledge, the Chinese company has decided to recall the ship," she said.
However, the shipping company said it could not confirm this.
It had been reported that the ship was headed for Angola, which is a close ally of President Robert Mugabe.
The Zimbabwe Electoral Commission says it cannot release the presidential results until a recount of 23 parliamentary results is completed.
The parliamentary results show that the ruling Zanu-PF party lost its majority for the first time since independence in 1980.
But this could change if the recount reverses the initial results.
So far, two recounts have been finished - both have confirmed the original results.
Much of the reported violence has been in rural areas which Zanu-PF has lost to the MDC in this election. The campaign for the 29 March election was relatively peaceful.

Source: BBC