Mugabe said homosexuality was “just madness … insanity”, and said gays were “destroying nationhood”.
Tsvangirai, speaking after Mugabe at a Women’s Day celebration event in Chitungwiza, said: “The President has spoken on the issue of gay rights, men who breathe to other men’s ears.
"Never, I don’t accept that culture. Why do you look for other men when women make up 52 percent of the population? Men are few.”
The two leaders, joined by Deputy Prime Minister Arthur Mutambara, were making their pitch on a controversial subject which is set to crop up when the country begins a process to draw a new constitution next month.
Amid cheers, Mugabe said: “Three days ago, I heard that some people want us to discuss the issue of gays in the new constitution. How do we even begin to talk about it?
“Those who engage in homosexual behaviour are just crazy. It’s just madness. Insanity. We can’t do it or the dead will turn in their graves.”
Mugabe said a family was made up of a “father, mother and children”, adding: "If you are doing that (engaging in homosexuality), you are destroying nationhood.”
He described homosexuality as an “alien practise that is being exported into our country”.
He added: “In Britain and the United States, I saw an archbishop blessing a gay wedding … I want to see how they will procreate. If they manage, then I will admit that I don’t know …”
Although gay rights are recognised in most western countries, same-sex relationships are fiercely opposed in much of Africa.
Zimbabwe begins a process of drafting a new constitution on April 10, and gay rights are set to be one of the most controversial proposals to be debated.