In his letter to parliament about the measure it passed and sent to him for signature, Museveni said "The proposed law should be clear so that what is thought to be criminalized is not the state of one having a deviant proclivity but rather the actions of one acting on that deviancy."
"The bill should be reviewed and include a provision that clearly states ... a person who is believed or alleged or suspected of being a homosexual who has not committed a sexual act with another person of the same sex does not commit an offence," the letter also stated.
He also asked lawmakers to remove provisions that impose a duty on citizens to report acts of homosexuality because it would create "constitutional challenges" and also be a source of conflict in society.
He stated the need to include a provision to facilitate rehabilitation of homosexuals who voluntarily renounce the practice. The country's deputy attorney general has also advised that a mandatory death penalty also be removed from the law.
The parliament's speaker Thomas Tayebwa referred the bill back to parliament's legal affairs committee which will process and report on it and return it to the full House for fresh debate and passage.
Once it is passed again by the full House it will be returned to the president for approval.
The law has stoked widespread criticism from human rights defenders, Western governments and corporations.