Days ago, Saied had warned that judicial actions must be taken against those who defame the "symbols of the state", considering that as an attack on state security.
The activists are Nejib Chebbi, Reda Belhaj and Ayachi Hammami. Chebbi is the leader of the opposition Salvation Front and has organised regular protests against Saied for months.
The justice ministry was not immediately available for comment.
Saied seized control of executive powers in July 2021 and later dissolved parliament, a step described by his opponents as a coup. Saied's opponents accuse him of imposing a dictatorship and strengthening one-man rule.
The powerful UGTT Union also criticised the president, saying that it rejects his autocratic approach and will not remain silent.
Hammami said a judge opened an investigation at the request of the justice minister on charges of spreading rumors and insulting the president. Hammami last week accused the authorities of fabricating terrorist cases against judges dismissed by Saied last year.
Chebbi said that he would not respond to any lawsuit because the case is politically motivated.
"It is a farce ... it is fabricated political file," Chebbi said.
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