Muhoozi Kainerugaba said "no-one will ban him from anything", despite President Yoweri Museveni having to issue a public apology and diplomatic meetings to reaffirm ties with Kenya following his son's comments two weeks ago.
General Kainerugaba passed off his suggestions that he would invade Kenya as a joke after being accused of jeopardising relations between the two countries, saying his father “told me never to attempt it”.
The president sacked his 48-year-old son as commander of the army's land forces following his comments. However, he promoted him to the rank of general and retained him as his adviser.
Earlier this week, the president said the general would steer clear of "talking about other countries and partisan politics of Uganda" on Twitter. It is widely believed he is expecting his son to succeed him as president.
In a tweet, Mr Kainerugaba said: “I hear some journalist from Kenya asked my father to ban me from Twitter? Is that some kind of joke?? I am an adult and NO ONE will ban me from anything!”
People took to the social media platform to express their incredulity.
"An adult? Are you sure?” said one.
Another added: "I remember when as a child I wanted to stay up late to watch The Bold and The Beautiful. I'd tell my elder siblings exactly the same thing – ‘I am an adult and no-one will remove me from this living room’. Problem is, I never knew what to do with the freedom I was given, I slept.”
In a series of tweets two weeks ago about Kenya, General Kainerugaba said he had spoken to Kenya's former president Uhuru Kenyatta, and expressed regret that he had stepped down at the end of his two terms in August.
"My only problem with my beloved big brother is that he didn't stand for a third term – we would have won easily," he said.