Tsvangirai, a longtime political rival of Mugabe who joined in the power-sharing government last year, expressed concurrence with the president's statements taking gay rights off the table for the constitution, which is currently in the early stages of discussion, the BBC reported Friday.
Homosexual acts are currently illegal under the country's laws.
"I totally agree with the president," Tsvangirai said.
Mugabe earlier said putting language in the constitution supporting gay rights "is not debatable, it's not up for discussion."
"It is just madness, insanity. The ancestors will turn in their graves should we allow this to happen," he said.
Chesterfield Samba, director of the Gays and Lesbians of Zimbabwe, said he is seeking clarification of the comments made by the leaders, but they initially seem "very worrying."
Samba said his group would be submitting language to the constitutional review commission.