Washington last week froze some aid programmes, as well as cancelling military air exercises and barring entry to the US for specific Ugandan officials involved in "human rights abuses", including against the gay community.
Signed by President Yoweri Museveni in February, the law calls for "repeat homosexuals" to be jailed for life, outlaws the promotion of homosexuality and obliges Ugandans to denounce gays to the authorities.
"Uganda considers this announcement by the US regrettable as some of the halted funding and programmes in Uganda are those that will affect the most vulnerable people that the US government purports to support and aims to protect," the foreign affairs ministry said in statement.
The White House said the legislation "runs counter to universal human rights and complicates our bilateral relationship".
Uganda's foreign ministry insisted relations would not be harmed.
"There are more areas of cooperation between the Uganda and the US, as the two countries continue to share a lot in common on both regional and international issues," the statement added.
Rights groups say the law has triggered a sharp increase in arrests and assaults of country's lesbian, gay, bisexual and transgender (LGBT) community.
Human Rights Watch (HRW) and Amnesty International said in a joint report last month the LGBT community had faced a "surge in human rights violations", with people being arrested, evicted or losing their jobs, and at least one transgender person has been murdered since the law was passed.
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