A TV news presenter has been named as the traditional kingdom of Tooro's new monarch but the late king's family claim he chose an heir.
Yoweri Museveni, 81, won disputed elections in January to extend his 40-year rule.
The Ugandan president’s son, notorious for explosive remarks on X, has ambitions to succeed his father.
Barbara Kyagulanyi, married to the opposition leader, says she refused to reveal her husband's whereabouts.
The losing presidential candidate calls for "peaceful change", saying Uganda's judiciary is not independent.
Yoweri Museveni has won a record seventh term in elections after promising that the fledgling oil sector will boost the economy.
Yoweri Museveni, 81, says he has brought stability to Uganda. His critics complain of political oppression.
President Museveni has about 75% of the vote with results in from more than half of all polling stations.
President Yoweri Museveni is in a commanding lead ahead of his main challenger, pop star-turned-politician Bobi Wine.