The anti-homosexuality bill was expected to be debated today but Speaker Edward Ssekandi Kiwanuk said there is no time to take up the bill in this session.
This means it is unclear what will happen next to the legislation.
A parliament spokeswoman told Associated Press that the bill could come up in the next session but it would take time for it to reach the floor.
MP Kakoba Onyango told the news service he believed the bill had taken a long time to be acted on because President Yoweri Museveni objects to it and because of worldwide criticism.
The bill, introduced by MP David Bahati, was designed to strengthen Uganda’s already-harsh laws against homosexuality.
Clauses called for the death penalty for “aggravated” homosexuality, while those who fail to report incidences to police would be jailed.
The bill received worldwide condemnation from countries, gay rights campaigners and human rights groups.
Speaking to Radio Netherlands Worldwide, Frank Muguisha of Sexual Minorities Uganda said: “Right now I would say that I am almost sure that the bill is not coming.”
Internet campaign group Avaaz, which collected 1.6 million signatures against the bill, said the news was a “victory for all Ugandans and people across the world who value human rights”.