Mugabe and opposition leader Morgan Tsvangirai agreed on September 15 to form a unity government. But that agreement has unravelled due to a fight over control of important ministries.
Mugabe, one of Africa’s longest-serving leaders, has come under increasing pressure to step down from Western countries, who say he has reneged on the deal in a bid to hold on to power.
Tutu also told the BBC in an interview that military force against Mugabe’s government should not be ruled out.
"How much more suffering is going to make us say ‘No we have given Mr Mugabe enough time?’," Tutu asked in an interview with the BBC’s Radio 4.
While regional countries Botswana and Zambia have taken a tough line against Mugabe, most African leaders, including influential neighbour South Africa, chair of regional grouping of nations SADC and a UN Security Council member, have stopped short of calling on him to quit.
South Africa had strong historic links with Mugabe, who provided support during the struggle against apartheid.
South Africa’s ruling African National Congress (ANC) leader Jacob Zuma called for a quick end to Zimbabwe’s political and economic crisis.
"The New Year must bring a speedy resolution to this utterly untenable situation," said Zuma in a Christmas message.
Zimbabweans were hoping a new leadership would rescue the economy. Instead Zimbabwe has sunk deeper into crisis as the stalemate drags on.
Hyper-inflation means prices double every day, a cholera epidemic has killed more than 1 100 people and the opposition has accused the ruling party of abducting its supporters, a charge it denies.
Tutu also criticised South Africa for not taking tougher stands at the United Nations against countries with a record of human rights abuses.
"And I have to say that I am deeply, deeply distressed that we should be found not on the side of the ones who are suffering," he said.
"I certainly am ashamed of what they’ve done in the United Nations."