The activists also want the government to block the controversial Anti-Homosexuality Bill, which will soon be introduced in parliament.
Sex Minorities Uganda’s executive director Frank Mugisha, in a statement issued on Wednesday, said they were appealing to government to end the abuse of gays.
"As we today mark 2012 International Day against Homophobia and Transphobia, the LGBTI community calls on the Parliament of Uganda to reject the Anti-Homosexuality Bill that is still pending in Parliament, that incites unnecessary hatred and violence in the communities where we live and makes us daily targets for hate crimes, making it impossible for us to live freely," he said.
The statement was issued to coincide with the International Day Against Homophobia and Transphobia.
Mugisha emphasised the need to punish those who abuse homosexuals because of their sexual orientation.
"We request government to punish any violence targeted towards Ugandans for their sexual orientation and identities, as human rights are inherent regardless of sexual orientation or gender identity," he said.
Gays in Uganda chose the theme, "Don’t punish love, punish violence to celebrate the day."
Mugisha said the theme was inspired by a statement from the United Nations High Commissioner for Human Rights Navi Pillay who urged countries to repeal discriminatory laws.
"Around the world, people are arrested, attacked, tortured and killed, just for being in a loving relationship," she said. "We cannot let these abuses stand."
The day is celebrated on May 17 every year because on the same date in 1990 the World Health Organization (WHO) removed homosexuality from its list of mental disorders.
"This action served to end more than a century of medical homophobia," Mugisha said. "The decision of the WHO constitutes a historic date for members of the community."
Ugandan gays and lesbians continue to experience hate speech, violence-inciting legislation, arrests, evictions, threats to life, arbitrary detention, blackmail, denial to services, loss of family and loss of property.
He added: "The LGBTI community, denounces the government’s complacent position and continued refusal to accord LGBTI Ugandans equal access to the human and civil rights every other Ugandan is entitled to under the constitution, and for continuing to make same sex relationships criminal.
Efforts to get comment from governmet officials about gays celebrating the day were fruitless.
Same sex relationships are regarded as taboo in conservative Uganda.