Colonel Major Ismael Wague, one of the junta's strongmen, accuses one of the deal's signatories, the Coordination of Azawad Movements (CMA) - an alliance of Tuareg-dominated independence and autonomist groups - of repeated violations of the 2015 Algiers agreement.
The letter, dated February 24, was addressed to Algerian Foreign Minister Ramtane Lamamra.
The letter questions the credibility of the international mediators supporting the agreement's implementation, which include the UN, African organizations and foreign partners under the leadership of Algeria.
"The behavior of certain movements is an obstacle to peace," the minister said.
He accused the CMA of "increasingly obvious collusion with terrorist groups".
"The government, while remaining committed to the intelligent implementation of the agreement, will automatically reject any accusation that would hold it responsible for the possible consequences of (its) violation," he warned.
It comes amid heightened tension between the junta, which seized power in 2020, and the signatories of the Algiers agreement, led by the CMA.
The Algiers agreement ended years of hostilities with groups which in 2012 mounted a campaign for independence in northern Mali - a conflict that was fanned by jihadists.
The accord provides for more local autonomy and the chance for former rebels to integrate their fighters into a state-run "reconstituted" army that would operate throughout the north.
The deal has often been touted as crucial for resolving tensions in the deeply troubled Mali, but delays in implementing it have fueled doubts about its future.
The jihadists, meanwhile, have continued to fight and the security crisis has spread to central Mali and neighboring Burkina Faso and Niger.
The CMA in December announced it was suspending its participation in the deal's implementation, accusing the junta of failing to uphold its side of the deal.
An official supporting the junta in February said he expected hostilities to resume soon.