Mr Saied said there were "errors in the form and others in the arrangement that have infiltrated the published draft", Tunisia's TAP news agency reported.
"Clarifications needed to be added to avoid confusion and interpretation," Mr Saied said in an official video released on the eve of Eid Al Adha.
Mr Saied has not previously commented on the constitution since he published its text. Under its provisions, the powers of the president would increase, while those of parliament and the judiciary would be diminished.
The proposed draft will be put to a referendum later this month. It is meant to replace the 2014 constitution that was drawn up by a constituent assembly after mass protests forced long-time leader Zine El Abidine Ben Ali to step down in 2011.
Mr Saied's updated version of the draft, published in the official gazette, makes changes to two articles, although it still retains a broad range of powers for the head of state.
Changes have been made to an article that said Tunisia "is part of the Islamic community" and that "the state must work to achieve the objectives of Islam" — it now adds the clause "within a democratic system".
The article had been criticised for its ambiguity by advocates of a completely secular system.
The other amendment was to an article about rights and freedoms, which now clarifies that "no restriction may be placed on the rights and freedoms guaranteed in this Constitution except by law and necessity imposed by a democratic order".
The rest of the document's 46 chapters remains largely unchanged. It will be put to a referendum on July 30.
At least two members of the drafting committee have highlighted alterations to the text they submitted to the president.
Sadok Belaid, a former constitutional law professor appointed by Mr Saied to draft a “new constitution for a new republic”, told the Assabeh newspaper that the version published in the official gazette was “dangerous” and could pave the way for “a disgraceful dictatorial regime”.
The biggest change is to the structure of the government, in which the presidency would be strengthened and parliament and the judiciary weakened.
As head of the executive, the president would propose legislation for approval by both parliament and a new legislative body called the National Council of Regions and Districts.
The new council, a long-time political project of Mr Saied, would be drawn from members of yet-to-be-formed local councils responsible for governing on a grass roots level.
Mr Saied insists this will put power back in the hands of the people and be a course correction after the 2011 revolution.
But the language in the new constitution grants sweeping powers to the president to dissolve both the legislature and government without an approval process or oversight. Additionally, there is no procedure provided for impeachment.
The new constitution would also reduce the power of the judiciary to a “function” of the state rather than a separate authority, and forbid judges to strike.