The cholera outbreak has followed a political crisis since elections in March and a subsequent failure to agree on a power-sharing deal.
Mugabe lost initial presidential elections to Morgan Tsvangirai, head of the opposition Movement for Democratic Change (MDC).
Tsvangirai pulled out of a second run-off poll in June due to attacks on his supporters which were blamed on Mugabe's allies, handing Mugabe victory.
Case for intervention
Earlier, in the Kenyan capital Nairobi, Odinga said that Jakaya Kikwete, Tanzania's president and chairman of the African Union, should call an urgent summit of AU states to formulate a resolution sending troops to Zimbabwe.
"If no troops are available, then the AU must allow the UN to send its forces into Zimbabwe ... to take control of the country and ensure urgent humanitarian assistance to the people dying of cholera and starvation," Odinga said.
|Mugabe's government has blamed EU sanctions for Zimbabwe's cholera epidemic [AFP]
Asked whether time for diplomacy had ended and military force should be used, Odinga told Al Jazeera: "Morgan Tsvangirai won the election decisively by garnering 56 per cent of the vote and the election commission was blackmailed into declaring that he didn't get the requisite 56 per cent.
"What we are trying to say is that, there is need for us to agree what we go back to what Zimbabweans said on the 29th of March - that they really wanted Mugabe out.
"Mugabe may not want to go, but the time has come for him to be shown the door. That's why I am appealing to the AU to live up to the expectations of the majority of the African people by asking Mr Mugabe to leave."
Odinga was himself involved in a bitter political tussle with Mwai Kibaki, Kenya's president, after he "lost" an election he is widely believed to have won.
A power-sharing agreement saw the government creating the current position he is holding.
EU sanctions blamed
Harare has blamed EU sanctions for a cholera outbreak across the country which is thought to have killed at least 575 people.
Mugabe accused Zimbabwe's former colonial ruler Britain of using the epidemic to draw together support against his government.
An editorial in the state-run Sunday Mail newspaper also said the outbreak was down to EU sanctions.
"The people who are suffering most are not politicians they claim they want to punish, but poor people," it said.
"All the victims [of cholera] are as a result of the freezing of balance of payments support, depriving the country of foreign currency required to buy chemicals to treat our drinking water."
Plea for pressure
Odinga's views echoed those expressed by Phandu Skelemani, Botswana's foreign minister, who said that the international community could easily force Mugabe out.
"SADC [Southern African Development Community] should never have recognised Mugabe as legitimate," Skelemani told Al Jazeera.
"The best solution would be to pressurise Mugabe as an international community to go for a [presidential] run-off. So that the Zimbabweans, the only ones entitled to choose a government for Zimbabwe, can do so."
|UK PM Brown has called Mugabe's government a 'blood-stained regime' [EPA]
"My suspicion is that Mugabe would not agree because he is sure to lose," Skelemani said, adding that, in such a situation, supplies to Mugabe should be cut off - for instance, petrol for his army.
Skelemani's comments followed those of Gordon Brown, the British prime minister, who said Mugabe's regime was "blood-stained" and Condoleezza Rice, the US secretary of state, who said that it is well past the time for Mugabe to quit.
EU foreign ministers are expected to adopt a draft text tightening sanctions against Zimbabwe on Monday, due to fears over the worsening humanitarian situation and political deadlock in the country.
Mugabe and his wife Grace, as well as 166 other members of the governing Zanu-PF, are already banned from entering EU nations and their European assets have been frozen.
This list is expected to be added to on Monday.