The East African nation adopted one of the world's harshest laws against homosexuality in May, prompting an uproar by rights advocates and Western powers, with U.S. President Joe Biden threatening to cut aid and investment to Kampala.
The legislation contains provisions making "aggravated homosexuality" a capital offense and imposes penalties for consensual same-sex relations of up to life in prison.
But President Yoweri Museveni's government has struck a defiant tone, with officials accusing the West of trying to pressure Africa into accepting homosexuality.
"We agreed to proceed with written submissions as opposed to oral submissions," Nicholas Opiyo, the lawyer representing the petitioners, told the court in Kampala on Monday.
"Court shall give judgement on notice," Uganda's deputy chief justice Richard Buteera, who is heading the panel of five judges at the constitutional court, said during Monday's hearing.
The petitioners calling for the law to be overturned include several human rights activists, two law professors from Makerere University in Kampala and two legislators from Museveni's National Resistance Movement party.
No date has been set for the ruling.
Washington this month imposed visa bans on unnamed officials deemed responsible for "undermining the democratic process" in Uganda and abusing human rights, including those of the LGBTQ community.
The United States has also announced plans to remove the country from the African Growth and Opportunity Act trade pact from January 2024.
The U.S., the European Union and U.N. chief Antonio Guterres have slammed the legislation, warning that foreign aid and investment for Uganda could be jeopardized unless the law is repealed.
But the law enjoys broad support in the conservative country, where lawmakers have defended the measures as a necessary bulwark against Western immorality.
Henry Okello Oryem, the Ugandan state minister for foreign affairs, told AFP earlier this month that the West was seeking "to coerce us into accepting same-sex relationships using aid and loans."
The World Bank announced in August it was suspending new loans to Uganda over the law, which "fundamentally contradicts" the values espoused by the U.S.-based lender.
In 2014, international donors slashed aid to Uganda after Museveni approved a bill that sought to impose life imprisonment for homosexual relations, which was later overturned.
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