Despite some changes, the new bill retains most of the harshest measures of the legislation adopted in March, which drew condemnation from the United States, European Union, United Nations and major corporations.
The legislation was amended to stipulate that merely identifying as LGBTQ is not a crime. It also revised a measure that obliged people to report homosexual activity to only require reporting when a child is involved.
The provisions retained in the new bill include the death penalty for so-called aggravated homosexuality and a 20-year sentence for "promoting" homosexuality, which activists say could criminalize any advocacy for the rights of lesbian, gay, bisexual, transgender and queer citizens.
Aggravated homosexuality includes having gay sex when HIV-positive.
The legislation now heads back to Museveni, who can sign it, veto it or return it again to parliament.
Western governments suspended aid, imposed visa restrictions and curtailed security cooperation in response to another anti-LGBTQ law Museveni signed in 2014. That law was nullified within months by a domestic court on procedural grounds.
The U.S. government said last week that it was assessing the implications of the looming law for activities in Uganda under its flagship HIV/AIDS program.
Museveni, a vocal opponent of LGBTQ rights, has signalled he intends to sign the legislation once certain changes are made, including measures to "rehabilitate" gay people.
It was not immediately clear if the new bill satisfied his requests, and his office was not available for comment.
