Opposition leader Bobi Wine remained in hiding on Friday after accusing security forces of raiding his home in the aftermath of the election on January 15.
He has described the election as "blatant theft" and called for protests.
Museveni, 81, won a seventh term in office with 72 percent of the vote to Wine's 25 percent, according to the Electoral Commission.
African observers and international NGOs criticised heavy repression of the opposition and an internet shutdown.
United Nations Secretary-General Antonio Guterres said Thursday he was "following with concern the post-election situation in Uganda, including reports of arrests, detentions and violent incidents involving opposition figures and supporters".
But army chief Muhoozi Kainerugaba boasted on Friday on X: "So far we have killed 30 NUP terrorists," referring to Wine's party, the National Unity Platform.
"We have arrested over 2,000 hooligans that Kabobi thought he would use," he added, using his nickname for Wine, whose real name is Robert Kyagulanyi.
The European Union also expressed concern on Friday, saying: "We regret pre- and post-electoral violence and threats, particularly against opposition leader Robert Kyagulanyi."
Kainerugaba, 51, is known for his provocative, often vulgar social media presence.
He has made no secret of his desire to succeed his father and this week threatened to hunt down and kill Wine.
He mixed his latest comments about the opposition with jokes about women.
Among those arrested in recent days is opposition lawmaker Muwanga Kivumbi from the Butambala area of central Uganda, where the most serious election day violence was reported.
Kivumbi told AFP that security forces had killed 10 of his campaign agents after storming his home, while police said his supporters had been shot after attempting to burn down a vote-tallying centre and police station.
A lawyer for the opposition told AFP on Wednesday that more than 600 people had been arrested over election protests.
"In all the charges, our clients are denying them. Some say they were picked up from their homes by the police and locked up before appearing (in court) on charges they were not aware of," lawyer Erias Lukwago told AFP.
str-er/kjm
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