In a letter to Museveni dated August 27, parliament speaker Rebecca Kadaga had called for the arrest of security personnel involved in the suspected beating and torture of 33 people after their arrest over the convoy incident.
"I am concerned that no effort has been made to arrest the security officers from the special forces command, military police and Uganda police force who were involved in the violent actions against unarmed civilians," Kadaga wrote.
"This is therefore to demand that the officers concerned be apprehended at the earliest opportunity and presented in court. The Uganda parliament will not condone or acquiesce in acts of torture."
The arrests sparked two days of anti-government protests in the capital Kampala and other towns last week.
Protesters and opposition supporters accuse Museveni, president since 1986, of stifling dissent through intimidation, beatings and detentions, charges which his government denies.
On Monday a Ugandan High Court granted bail to all 33 people arrested over the stoning.