The following is an excerpt of a BBC report:
The petition is the latest attempt to halt the bill, which carries the death penalty for some homosexual acts.
US President Barack Obama has called the proposed legislation "odious".
The European Union has also condemned the bill, as did Britain's Africa minister, Baroness Kinnock, when she visited Uganda last week.
The petition was delivered by counsellors, who could face jail for failing to inform the authorities if somebody confided their homosexual activities to them.
"This is a bill that requires various members of community, family members, service providers and spiritual mentors to "spy" on one another," a letter accompanying the petition reads.
The campaign is being led by Anglican priest Canon Gideon Byamugisha and he has been joined by HIV/Aids activists and civic organisations.
Campaign group Avaaz, which organised the online petition, hopes to get one million signatures.
Meanwhile, Uganda's New Vision newspaper reported on Mar 1 that the Speaker of Parliament, Edward Ssekandi, has told those opposing the Anti-Homosexuality Bill that it will not be withdrawn.