Two people were killed when his supporters rioted in the capital Kampala on Friday.
Dr Besigye is being treated in Kenya after being doused with pepper spray.
He has still not recovered his sight since police smashed through the window of his car with the butt of a gun on Thursday and sprayed him at close range, the incident caught on camera.
The opposition politician was then bundled into the back of a pick-up truck and driven off at speed, before being freed on bail for medical treatment.
April's walk-to-work campaign, organised by several opposition parties over rising fuel and food prices, has been marked by clashes between protesters and the police and the arrest of opposition politicians.
Museveni interrupted Uganda's inter-religious council accused the police of using brutal force against demonstrators and condemned the manner of Dr Besigye's arrest.
AnalysisThey prospect of a dialogue between the opposition and the government seems highly unlikely for now.
The opposition has pledged to continue the walk-to-work protests and is gaining political mileage by exposing the brutality of the police and military. The government of President Yoweri Museveni appears, to many, to be out of touch with the population which is suffering as inflation soars.
Dr Besigye has lost three disputed elections to President Museveni. The two men have not spoken to each other for ten years.
For now the streets of Kampala are quiet. President Museveni has been speaking at an event in the Kenyan capital Nairobi and by coincidence that is exactly where Dr Besigye is receiving medical treatment.
The chances of the two meeting in Kenya are slim to non-existent. The likelihood of more violence on Uganda's streets in the coming days remains high.
President Museveni, who happened also to be in Nairobi on Saturday, was interrupted by a protester while delivering a speech at a business club.
"Mr President, how can we as Kenyans sit here and listen to you while you have been brutalising Ugandans?" the man shouted, before being taken away by Mr Museveni's security detail.
The Ugandan leader said Dr Besigye could walk to work if he wanted to as long as he informed the police to "agree with them where he wants to pass".
"Kampala is a very crowded city," he said. He also described Friday's rioters as "looters".
Dr Besigye, who was shot in the hand during a similar recent protest, lost to Mr Museveni in a February election he says was rigged.
Before the polls, Dr Besigye had called for Egypt-style uprisings in the event of fraud.
Police responded by banning public demonstrations.