Ankunda said the detainees were “linked to a rebel group” that he declined to name.
He said most of those arrested were soldiers, adding that at least one lawmaker and another opposition politician had been arrested.
The only detainee named by the army spokesman was Michael Kabaziguruka, an MP from the main opposition Forum for Democratic Change (FDC) party whose leader Kizza Besigye is in custody facing treason charges.
Besigye, who claimed fraud after coming second to Museveni in February’s presidential election, was arrested last month for holding a mock swearing-in ceremony.
Besigye was previously charged with treason in 2005 but the case was eventually abandoned.
At the time prosecutors accused him of leading a shadowy rebel group named the People’s Redemption Army, a charge Besigye always denied.
“He told me he was questioned on rebel links, which he didn’t know about,” said Nganda, adding that other party supporters “are under detention on the same claim”.
Daily Monitor said one of the arrested soldiers is a captain responsible for the armoury at Bombo Military Barracks, the army headquarters north of the capital Kampala.