"I met with religious leaders and elders and accepted their demand for ceasefire and reconciliation with the opposition members, and I call on all opposition parties to halt the unnecessary violence," Ahmed said.
Arale said his group had met with the mediators but only discussed plans for a partial withdrawal of rebel fighters.
Sunday's rejection comes a day after Omar Abdirahsid Sharmarke, the Somali prime minister, led the inaugural session of the new government in Mogadishu, Somalia's capital.
It also follows renewed heavy fighting in Mogadishu between opposition fighters and government and African Union forces.
At least 49 civilians were killed in the clashes in the capital, the independent Elman Human Rights Organisation has said.
Hizbul Islam is against the presence of AU troops in Somalia and has said it will battle them until they leave the country.