"The Call of February 20" movement said in a statement sent to AFP on Monday that the army had no mandate "to plunge us into the unknown, or even to submit us to a state of no-rule of law."
The statement said the referendum was "illegal" and superfluous and demanded a vote for an early return of a civilian government in the insurgency-wracked west African nation.
The movement said the draft "seriously" threatens the independence of the judiciary and "organizes impunity for certain personalities."
According to the draft, any coup is an "inalienable crime," but it extends an amnesty to the colonels who seized power nearly three years ago.
The draft would also significantly strengthen the power of the president.
The movement said "no condition is right" to stage a referendum in a nation which does not control "more than two-thirds" of its territory, a claim the junta rejects.
"Without any doubt, we will prevent by legal means the holding of this irregular referendum," the movement vowed.
Mali "does not face a problem with the constitution, the only alternative is to turn the page on this transition which is as disconnected to the principles of the rule of law as it is to republican values."
The Call of February 20 is a bid by several groups and figures who have kept their distance from the military authorities to bring together political parties and civil society organizations.