Abdu-Latif Ssebagala, a Member of Ugandan Parliamentary Committee formed in September to draft a new version anti-gay law, said the drafters of a revised law wanted the parliament to pass it in time to be a "Christmas gift" for Ugandans.
He said on Friday in Kampala that a new anti-gay law was coming after a controversial earlier version was quashed because of legal technicalities.
Legislation passed by parliament almost a year ago, which would have punished gay sex with long prison terms, provoked a storm of international protest and led some donor countries to withhold aid.
A constitutional court overturned the law in August.
Ssebagala said it had finished the bill and was ready to present it to parliament for debate.
"The draft is ready and we have strengthened the law, especially in areas of promotion and luring children,'' he said.
"Next week, we expect to meet the speaker to fix a date for the re-tabling to parliament," he added.
Ssebagala said the committee wanted it passed within weeks so that Ugandans "can celebrate it as a Christmas gift".
"The earlier version would have punished gay sex with long prison terms, including life sentences for "aggravated homosexuality," he said.
"The latter category included an HIV-positive person having gay sex or gay sex with anyone vulnerable, such as when the victim is disabled or a child in the perpetrator's care,'' he added.
In August, President Yoweri Museveni,said he wanted the law amended to remove penalties for consenting adults.
Ssebagala, however, said the new version still punished gay sex among consenting adults.
In October, the president wrote in a newspaper that re-introducing the law risked triggering a trade boycott by the West.
Analysts say Museveni was expected to run for re-election in 2016 and was walking a tightrope trying to appease his conservative domestic constituency, while wary of alienating donors who finance about 20 per cent of Uganda's budget.
Asia Russell, Uganda-based Director of International Policy at Health GAP, an HIV advocacy group, said the bill was inconsistent with fundamental freedoms and human rights.
He insisted that accepting it would be a display of weakness rather than leadership.
Like most of sub-Saharan Africa, Uganda is highly religious and socially conservative.
Influential evangelical pastors have urged Ugandan legislators to reintroduce the law since it was quashed.
Presidential Spokesman Tamale Mirundisaid Museveni "is a democrat" and could not dictate to parliament what to do.
"We'll only know his views when the new law is passed and is sent to him for signing," he said.
The constitutional court overturned the earlier law on the grounds parliament had passed it without the required quorum.
Photo Credit: Getty Images/Peter Macdiarmid