Homosexual acts are already illegal in Uganda
Campaigners opposing Uganda's Anti-Homosexuality Bill have taken an online petition to parliament, signed by some 450,000 people from around the world.
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.
For "serial offenders", HIV-positive "offenders", or those engaging in homosexual activity with a minor or disabled person
Life in prison
Seven years in prison
For helping, counselling, or encouraging a person to engage in a homosexual act
"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.
However BBC East Africa correspondent Will Ross says the fact that the vast majority of the signatures were from outside Uganda is significant, as the MPs would be more likely to take notice of Ugandan rather than international opposition to the bill.
He says Uganda, like many African countries, is deeply conservative and Ugandan voices opposed to the bill are few and far between.
Homosexual acts are already illegal in Uganda - the bill proposes increasing the penalties for homosexual acts from 14 years in prison to life.
It also proposes the death penalty for a new offence of "aggravated homosexuality" - defined as when one of the participants is a minor, HIV-positive, disabled or a "serial offender".
The government has indicated it expects the final bill to be watered down.
However, it is a private member's bill and so the government says it cannot directly intervene before parliament votes on it.
The bill's sponsor David Bahati says he is trying to defend Uganda's culture.