The two parties met with the National Peace Council which is the referee to dialogue to end the vigilante groups.
The meeting was meant to establish the rules of engagement and the modalities for disbanding the groups.
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The crunch meeting was chaired by Nana Dr S. K. B. Asante, a member of the NPC and Omanhene of the Asokore Traditional Area in the Ashanti Region.
The delegation from the NPP was led by its National Chairman, Freddie Blay, and included stalwarts of the party.
The General Secretary, John Boadu; the National Organiser, Sammy Awuku; the Minister for Regional Re-organisation and Development, Dan Botwe; the Communications Director, Yaw Buabeng Asamoah, and a member of the communications team, Gary Nimako.
The NDC delegation was led by the National Chairman of the party, Samuel Ofosu-Ampofo, with the General Secretary, Johnson Asiedu Nketia.
Other members were a former Chief of Staff, Prosper Bani; a former National Security Minister, Kofi Totobi Kwakye; as well as the party's lawyers, Abraham Amaliba and Nana Ato Dadzie.
Among notable members of the NPC at the meeting were the Presiding Archbishop and General Overseer of the Action Chapel International, Archbishop Nicholas Duncan-William, and a former National Chairman of the Church of Pentecost, Apostle Professor Opoku Onyinah.
A communique issued at the end of the meeting said the parties had agreed that vigilantism was inimical to the country's democracy and ought to be tackled head-on.
"With respect to the immediate focus of the mediation or dialogue."
This comes after President Nana Addo Dankwa Akufo-Addo has added his voice to the calls by Ghanaians to disband all vigilante groups as a matter of urgency.
In his State of the Nation's Address on Thursday in Parliament, he said "I have asked the leadership of the NPP to extend an invitation to the leadership of the NDC for such a meeting on vigilantism. The security services of the country will be on standby to assist this meeting.
"If voluntary disbandment by the parties is not feasible, then I will initiate legislation on the matter. Vigorous debate and the exchange of ideas should be the true basis of political dialogue and competition in our country, not the activities of party vigilante groups."