His comments come on the back of a press statement released by the office of Mahama denying the involvement of the Asantehene in his decision urging the losing candidate to concede defeat in the 2016 elections.
The Asantehene, Otumfuo Osei Tutu in a speech at the United Nations conference over the weekend said his intervention in the 2016 polls, persuaded Mahama to accept defeat.
But Otumfuo's claim has been vehemently denied by the National Democratic Congress (NDC).
The claims by the Asantehene was met with some backlash from some section of the public, most sympathizers and supporters of the NDC.
Rawlings adding his voice to the backlash on the Asantehene's address said "comments by former President John Mahama on an aspect of the address shouldn't elicit or provoke an edict sounding threat.
"It's unwarranted and unnecessary. There's enough tension. Let's cool it and cool off".
"The Asantehene has made us proud with a highly educative address to the UN on the subject of PEACE. Comments by former President Mahama on an aspect of the address shouldn't elicit or provoke edict sounding threats....", he wrote on his Twitter handle.