"Tunisia is a free and independent state and there can be no interference in its affairs," he said at the first meeting of a new cabinet following his July power grab.
"Some have used refuge abroad to attack Tunisian interests."
Without naming him, Saied referred to a speech by France-based former president Moncef Marzouki, who has called the president's moves a "coup d'etat".
Addressing anti-Saied demonstrators in Paris on Saturday, Marzouki -- Tunisian leader from 2011-2014 -- urged the French government to "reject any support for this regime and this man who has plotted against the revolution and abolished the constitution".
"Democratic France should not be on the side of the dictatorial regime," the former president said, in a speech that was filmed and widely shared online.
Saied on July 25 sacked the government and froze parliament, moving later to rule by presidential decree before last month naming geologist Najla Bouden as prime minister.
The president earlier this month named a government.
Saied on Thursday accused "traitors that seek refuge overseas" of threatening Tunisia's sovereignty and urged the new Justice Minister Leila Jaffel to open an enquiry.
"He that did this will have his diplomatic passport revoked as he is the greatest enemy of Tunisia," he said.
"He cannot use this privilege to visit capitals and damage Tunisian interests."
Saied also met US Ambassador Donald Blome on Thursday, coinciding with a congressional meeting entitled "Tunisia: Examining the State of Democracy and Next Steps for US Policy".
The president "informed (Blome) of the State of Tunisia's annoyance at the situation in Tunisia being included in the proceedings of the American Congress", the presidency's Facebook page said.
“Some of Saied's opponents have accused him of seeking a new dictatorship, a decade after Tunisia's 2011 revolt that overthrew dictator Zine El Abidine Ben Ali,” said AFP.
But the president's supporters say his moves were needed after years of deadlock among political parties seen as corrupt and self-serving.