Mugabe, who formed a unity government with Tsvangirai in February, told hundreds of mourners at a memorial service in Harare that Susan Tsvangirai’s death in a car crash last Friday was an act of God.
"This is a difficult moment for our colleague. He has lost a partner and we must all rally to support him and lessen his burden … This is the hand of God," Mugabe said at the service for the woman who supported Tsvangirai through years of political struggle against the veteran president.
"To our supporters, we want to say violence should stop. That’s what (Mrs) Tsvangirai would have wanted, for us to co-exist peacefully. We have just started a new life after years of fighting each other and insulting each other. We have said let’s give peace and harmony a chance and work together."
Tsvangirai, who turned 57 on Tuesday, has ruled out foul play as the cause of a car crash that injured him and killed his wife, easing concerns that it would increase tensions in the new government. Many Zimbabweans had been suspicious of the cause.
Later, thousands of mostly MDC supporters including government officials and diplomats bade farewell to Susan Tsvangirai at a stadium adorned with huge pictures of Susan.
Tsvangirai’s oldest son Edwin thanked Mugabe for his speech.
"I want to thank His Excellency the president for words that changed my understanding of him," he told the crowd.
Tsvangirai already faced almost insurmountable challenges, even before his personal tragedy.
The International Monetary Fund said on Tuesday it could not disburse funding that Zimbabwe desperately needs until it clears its arrears and demonstrates responsible economic policies.
The IMF’s director for Africa, Antoinette Sayeh, denied media reports that an IMF mission currently in Zimbabwe — the first in two years — was discussing financial assistance.
"The Fund is not in a position to disburse resources to Zimbabwe, among other things, because Zimbabwe is in arrears," she told Reuters on the sidelines of an IMF conference in the Tanzanian capital.
Zimbabwe, beset by 90 percent unemployment, hyperinflation and shortages of the most basic goods, badly needs Western donors and foreign investors to rescue its economy.
But their help will be conditional on the implementation of fully democratic government and reforms such as reversing plans for nationalisation.
Sayeh said any lending would depend on support from other donors and agreement on an economic program "which credibly begins to address Zimbabwe’s very, very serious problems".
"So all of that is to come. We’re merely doing a stock-taking of recent developments in Zimbabwe with this mission that will report to our board when it returns to Washington," Sayeh added.
Economic Planning Minister Elton Mangoma earlier told Reuters Zimbabwe had no means of paying arrears to the Fund.
The IMF suspended Zimbabwe’s voting rights in June 2003 as its economy deteriorated and the Mugabe government fell behind on debt repayment.
The IMF says it was owed $89 million at the end of February 2009. The World Bank says Harare owes it $600 million, and the African Development Bank says it was owed $429 million as of the end of June last year.
Despite describing the talks as "cordial", Mangoma backed away from earlier comments reported in the state-controlled Herald newspaper suggesting the IMF and World Bank had agreed to a meeting next month to hammer out an aid package.