"Through (an) intelligence network, we have arrested the six men in a room in Jinja city where they were practicing homosexuality," police spokesman James Mubi said.
"We have been informed the six were part of the larger group in Jinja engaging in acts of homosexuality and we are appealing to the public to provide police with information leading to the arrest of the remaining members of the group."
Jinja lies 80 kilometers east of the capital Kampala.
Uganda is notorious for intolerance of homosexuality, which is criminalized under colonial-era laws, and for strict Christian views on sexuality in general.
On Thursday, addressing lawmakers who are preparing to discuss anti-gay legislation, Museveni said "homosexuals are deviations from normal."
"Why? Is it by nature or nurture?" the 78-year-old asked.
"We need to answer these questions," he said. "We need a medical opinion on that. We shall discuss it thoroughly."
Under the proposed law, anyone who engages in same-sex activity or who identifies as LGBTQ could face up to 10 years' imprisonment.
The bill is due to be discussed next week, with a vote possible as early as Tuesday.
It comes as conspiracy theories accusing shadowy international forces of promoting homosexuality gain traction on social media in Uganda.
There has never been a conviction for consensual same-sex activity in Uganda since the country gained independence from Britain in 1962 .
In 2014, Ugandan lawmakers passed a bill that called for life in prison for people caught having gay sex.
A court later struck down the law on a technicality, but it had already sparked international condemnation, some Western nations freezing or redirecting millions of dollars of government aid in response.
Uganda Arrests Men for 'Practicing Homosexuality'
KAMPALA - Uganda's police said Friday they had arrested six men for "practicing homosexuality", an announcement that came a day after President Yoweri Museveni described gay people as "deviations."
