The council is pleading with the President, John Dramani Mahama to grant the three presidential pardon.
Members of the council on Monday signed the petition book opened by the free Montie movement.
The movement hopes to gather 1million signatures with which they would petition the President.
Acting president of the Ga traditional council Nii Dodoo Nsaki II told the press after signing the petition, the president has to respond to the overwhelming appeal for mercy.
The contemnors Alistair Nelson, Godwin Ako Gunn, and Salifu Maase, alias Mugabe are currently serving a four-month jail term for contempt.
They were hauled before the Supreme Court for scandalizing the apex court and also bringing its name into disrepute after threatening to kill justices of the bench.
Many government appointees, ministers and deputy ministers including Gender, Children and Social Protection Minister Nana Oye Lithur, Deputy Minister of Education Samuel Okudzeto Ablakwa, Deputy Petroleum Minister Benjamin Dagadu, Tourism Minister Elizabeth Ofosu-Adjare, Deputy Chief of Staff Valerie Sawyerr and the PRO of the Accra Metropolitan Assembly Numo Blafo III have joined the group of individuals and NDC party faithful mounting pressure on the President to invoke his prerogative of mercy powers guaranteed under Article 72 towards freeing the three convicts who made the threats on Accra-based Montie FM.
Meanwhile, the President’s Lawyer, Tony Lithur has said it would be reckless for the president to barge.