MPs in the African nation are considering an Anti-Homosexuality Bill, which would impose harsh penalties for â€śaggravated homosexualityâ€ť.
The original version of the bill stipulated the death penalty, but this has reportedly been dropped.
In his latest comments at the swearing in of a new head of the Anglican Church of Uganda, the president was careful to neither condemn the bill nor openly support it, BBC reports.
Yoweri Museveni said: "If there are some homosexuals, we shall not kill or persecute them but there should be no promotion of homosexuality.
"We cannot accept promotion of homosexuality as if it is a good thing."
Speaker of Parliament Rebecca Kadaga recently said the bill would be passed as a "Christmas gift" to its supporters.
However, Parliament has adjourned until January without voting on it.