"Conflict is usually ignited easily when division of whatever nature blurs common vision and creates suspicion and mistrust in society.
"Through reconciliation, tolerance and forgiveness, the sky should be the limit for your aspirations," Moi told the Sudanese political groups gathered in Nairobi for the reconciliation dialogue.
Representatives attending the meeting are former southern Sudan rebel leaders, pro-Khartoum government militias and other armed groups.
Moi urged the Sudanese political elite, including the leader of the Sudan Peoples Liberation Movement (SPLM) John Garang, to embrace dialogue as a key investment for peace to help bridge their ideological differences.
"I call upon you to relinquish all divisive tags and accommodate each other. This will help you to cultivate a collective sense of responsibility as a way of transcending beyond fault lines in your society," he told over 200 participants who also included civil society organisations.
The three-day conference, dubbed South-South Dialogue, is being convened by Moi's charitable organisation, the Moi African Institute, to facilitate the achievement of a viable political settlement to the tension arising from the 9 January peace accord.