"We want the National Assembly to amend the electoral laws so that local government elections will henceforth be organised by INEC (Independent National Electoral Commission of Nigeria)," a coalition of 16 parties said in a statement.
It said state governments were rigging local polls to secure victory for the ruling party in the province.
The group cited the October 8 local government election in the southwestern Ogun state which it said was rigged by the All Progressives Congress (APC) of President Muhammadu Buhari.
The coalition, including the main opposition People's Democratic Party (PDP), Unity Party of Nigeria (UPN), Alliance for Democracy (AD) and the Labour Party, said the APC was declared winner in all the 20 local government and 37 community development areas in Ogun state.
"It is obvious that the state electoral body could not conduct a credible poll. We therefore call on the National Assembly to review the section of the constitution that empowers the state governments to conduct local government elections with a view to avoiding a rape of our democracy," it said.
Otunba Rotimi Paseda, who signed the statement on behalf of the coalition, said the Ogun vote was marred by intimidation, rigging and violence.
Paseda said electoral fraud was so glaring that the opposition party agents refused to sign the result sheets and called for the results to be annulled.