Issam Chebbi, head of the Republican Party, was detained near a shopping center while he was out with his wife, his family and lawyers told Reuters. Police later searched his home.
Chaima Issa, an activist who took part in the 2011 revolution, was detained after police surrounded her in her car, her lawyer Samir Dilou said.
Issa was already facing a military tribunal on charges of insulting Saied but had refused to answer questions during her court appearance, saying she should be tried by a civilian judge.
Police also surrounded the house of Jawher Ben Mbarek to detain him, but the constitutional law professor was not there, his sister and lawyers said.
The arrests, along with others this month, have targeted some of Saied's most important critics along with other politicians, judges and media figures.
Speaking in a video published online on Wednesday, Saied attacked the National Salvation Front opposition coalition in which Ben Mbarek and Issa were leaders, along with Chebbi's brother.
Saied called it "a paid campaign", adding that "Tunisia wants to get rid of these criminals."
The president has said the moves were legal and necessary to save Tunisia from chaos, repeatedly calling his critics traitors and enemies of the state.
The police and Interior Ministry have declined to comment on the arrests, but lawyers have said some of those detained were accused of conspiring against state security.
Saied had previously said that some of those arrested were responsible for shortages of food and fuel that economists have blamed on a crisis in public finances.