The new legislation criminalises the promotion of homosexuality and comprises a potential life sentence for performing gay sex, including oral sex.
Homosexuality was already illegal in Uganda.
The Ugandan leader said he was persuaded to sign the bill, which was passed by its parliament last year, after he consulted, among others, scientists and medical experts who said homosexuality was behavioural, not genetic ‘and could be unlearnt’.
At the signing of the bill, he maintained: ‘Since nurture is the main cause of homosexuality, then society can do something about it to discourage the trends.’
She writes: '[I] request that you give every consideration to the withdrawal of this piece of legislation at the earliest opportunity.'
She has also questioned the science and alleged medical expertise used to support the legislation.
She said: ‘It is deeply disturbing that any country should pass legislation enacting discrimination against any group — in this case homosexuals.
‘It is equally disturbing that the legislature was aided by so-called medical experts who reinforced bad science and prejudice.’
The new anti-homosexuality laws have been widely criticised across the world.
The World Bank last week suspended a £54m loan to the Ugandan health sector owing to the anti-gay laws.
Norway has said that, as a result, it is redirecting millions in aid for Uganda towards human rights and democracy organisations.
Dutch aid has also been suspended and Denmark has said it is ‘restructuring aid away from the government’.
The World Medical Association, whose president is Ugandan psychiatrist Margaret Mungherera, has also sent a letter to Mr Museveni on the issue.