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.
The BBC reports that 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. 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 said it cannot directly intervene before parliament votes on it.
The bill's sponsor David Bahati said he is trying to defend Uganda's culture.
