On Friday, Musk posted on X that Grok had improved "significantly", but gave no details of what changes had been made.
"You should notice a difference when you ask Grok questions," he added.
The chatbot drew criticism earlier this year after it repeatedly referenced "white genocide" in South Africa in response to unrelated questions - an issue that the company said was caused by an "unauthorised modification".
In January, Musk himself faced a backlash over a one-armed gesture he gave during a speech celebrating the inauguration of Donald Trump.
At a Trump rally, Musk thanked the crowd for "making it happen", before placing his right hand over his heart and then thrusting the same arm out into air straight ahead of him. He then turned and repeated the action for those sitting behind him.
Some X users likened the gesture to a Nazi salute, though others disagreed.
In response, the SpaceX and Tesla chief posted on X: "Frankly, they need better dirty tricks. The 'everyone is Hitler' attack is sooo tired."
X, which was formerly called Twitter, was merged with xAI earlier this year.
Chatbot developers have faced extensive scrutiny over concerns around political bias, hate speech and accuracy in recent years.
Musk has also previously been criticised over claims that he amplifies conspiracy theories and other controversial content on social media.