Tunisian President Kais Saied. AFP
The North African country's main opposition coalition had pressed the government earlier to explain Saied's public "absence", saying it had information that he was sick.
"These people deserve nothing but contempt," Saied said in the video, referring to his political rivals.
"The president is absent for two or three days, he gets a cold and that becomes a problem, a power vacuum?"
Saied, 65, had not appeared in public or held any meetings since March 22, according to posts on Facebook, the presidency's only official channel of communication.
The lack of statements or videos has sparked rumours over the state of Saied's health.
Speaking alongside Prime Minister Najla Bouden, the president said the reports reflected "a level of madness never seen before in Tunisia".
Earlier on Monday, Ahmed Nejib Chebbi of the National Salvation Front opposition coalition told journalists: "We ask the government to address the Tunisian people and say if the president has health problems that have forced him to be absent."
Chebbi said Bouden would run Tunisia in the event of a temporary power vacuum, but that a permanent vacancy would present the country with a "great catastrophe" due to a legislative void.
In his video, Saied accused unnamed people of "trying to create crises" by talking of a power vacuum.
"These people have lost the plot, they're obsessed with power," he said.
Saied, who ruled by decree in July 2021, last year rammed through a constitution giving his office unlimited powers and neutering parliament.
Since February, security forces have arrested over 20 public figures, including top members of the opposition.
Those targeted include members of the once-powerful Islamist-inspired Ennahdha party and political activists, as well as lawyers, businessmen and the head of a popular radio station known for giving a platform to criticism of the president.
Saied has publicly alleged they were plotting against the state and labelled them "terrorists".
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