Museveni tweeted that Mwesigwa Rukutana, Minister of State for Labour, who was arrested on September 5 after a video circulated on social media showing him grab a gun from a police officer, would answer for his charges, reports Xinhua news agency.
The video shows that after the Minister grabbed the gun to attack his rivals, but the latter managed to escape.
Rukutana had just lost an election in the ruling National Resistance Movement (NRM) party primaries for legislators held the previous day.
The Minister and his three body guards are facing charges of inciting violence, attempted murder by shooting, and malicious damage of property, according to police.
The party primaries were marred by violence in some parts of the country.
Museveni said all those who caused violence or engaged in some form of illegality would be arrested and prosecuted.
"Those who beat people... are all in jail or on the run. Minister Rukutana is in jail and will be prosecuted.
"They will be fully accountable with robust charges: assault, attempted murder, murder, etc.," the President added.
The primaries were held as different political parties in the country are preparing for next year's general elections.
The NRM party in July declared Museveni as the party's presidential candidate in the 2021 general elections.
He will be running for another term of office after about 35 years in power.
Museveni is expected to face off with Robert Kyagulanyi, a music icon turned politician, in what is anticipated to be a hotly contested election.
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