Ugandan gay people have long alleged persecution
A Ugandan MP has proposed creating an offence of "aggravated homosexuality" to be punishable by death.
Ruling party MP David Bahati wants the death penalty for those having gay sex with disabled people, under-18s or when the accused is HIV-positive.
Homosexual acts are already illegal, but the Anti-Homosexuality Bill proposes new offences and urges the toughening of existing penalties.
Earlier versions of the bill were widely criticised by rights groups.
The BBC's Joshua Mmali, in the capital Kampala, says the bill has a good chance of being passed as senior figures from the ruling National Resistance Movement are likely to back it.
President Yoweri Museveni has made several speeches outlining his own anti-gay views.
There are estimated to be 500,000 gay people in Uganda, from a population of about 31 million, according to gay rights groups.
Gay activists have long alleged persecution and existing laws already allow large fines and life imprisonment for some homosexual acts.
Mr Bahati's bill proposes widening the definition of homosexual acts and wants to fine or imprison anyone found to be promoting homosexuality.
The bill states that its provisions are intended to "protect the traditional family by prohibiting any form of sexual relations between persons of the same sex".
The International Gay and Lesbian Human Rights Commission has urged the bill to be dismissed.
They say it violates several international agreements Uganda has signed up to - as well as contradicting the country's own constitution.
But John Otekat Emile, an independent MP, said he believed the bill had a "99% chance" of being passed.
"Members of parliament are overwhelmingly supporting this bill because homosexuality is illegal in Uganda, and we have that clearly in the penal code," he told the BBC.
Emmanuel Dombo, an MP with the ruling party, agreed and said it was an important issue to investigate.
"What we need to look at are the sentences - what kind of sentences or punishment should be prescribed for sexual offenders in this respect - that is the big question," he said.
But our correspondent says the authorities already find it difficult to prove cases under current laws because evidence is difficult to obtain.
Some people who have openly declared that they are gay have not been prosecuted because declaring sexual orientation is not a crime, our correspondent adds.