"I am not poisoned, I am well," he said on a video released on Monday evening.
At the weekend, the king's traditional prime minister said he had gone to neighbouring Eswatini for treatment.
Chief Mangosuthu Buthelezi added that it followed the sudden death of one of the king's senior advisers, also of suspected poisoning.
But in response, the king's spokesperson, Prince Africa Zulu alleged there was "an orchestrated agenda and a desperate narrative to communicate defamatory and baseless claims of His Majesty's ill-health".
The dispute is a sign of how the relationship between King Misuzulu and Chief Buthelezi has fallen apart, reports the BBC's Nomsa Maseko in Johannesburg.
But in a strongly worded statement on Tuesday, Chief Buthelezi said there was "certainly no growing rift" between him and the king. He did acknowledge that there were "disagreements on matters from time to time", but this was "like any other family".
Chief Buthelezi added that he had not "acted in malice by making the announcement about his health".
In the video released on Monday, the king, looking well, explained that he had travelled to Eswatini for a regular medical health check - something that Chief Buthelezi continues to dispute saying that the king crossed the border to "urgently seek medical attention".
"I'm happy, everything is well-functioning, there is no poison whatsoever. So please people, mostly to the Zulu people, the Zulu royal family also to remind everyone to please don't listen to everything that people say," the king said.
King Misuzulu was crowned in front of thousands of his subjects last October.
But a vicious power struggle has been raging within the royal family over the 48-year-old's accession, while tensions have also recently surfaced between the monarch and Chief Buthelezi.
The Zulu king does not have formal political power and the monarch's role within broader South African society is largely ceremonial, but he remains hugely influential with a yearly government-funded budget of several million dollars.
King Misuzulu's accession to the throne was sooner than expected and he has been at the centre of palace intrigue.
His father died during the Covid pandemic in March 2021 of diabetes-related complications.
He was the Zulu nation's longest-reigning monarch, having served on the throne for almost 50 years.
King Misuzulu's mother, Queen Mantfombi Dlamini-Zulu, then became the regent, but she died a month later.
She was the sister of Eswatini's King Mswati III - Africa's only absolute monarch.
At the time, Chief Buthelezi dismissed rumours that she had been poisoned.
He had backed King Misuzulu's accession to the throne after her death, but recent reports suggested that sharp differences had emerged between the two.
It followed a dispute over the chairmanship of the Ingonyama Trust Board, which manages vast tracts of land controlled by the monarch.
The king appointed Chief Thanduyise Mzimela as its chairman, but this was opposed by Chief Buthelezi who felt he was inexperienced for the post, according to local media.
Source: BBC