Jega made the call during a debate on ethics and elections organised by the Friedrich Ebert Foundation on Tuesday in Abuja.
The chairman said the tribunal would help restore sanity to the country’s electoral process and deter people from committing electoral offences.
Jega said: “I was privileged to serve in the Justice Muhammad Lawal Uwais-led Committee and I know we made a recommendation for the establishment of a tribunal to deal with the impunity in the way electoral offences are being committed in Nigeria.
“We need to do something unique and that is to establish an electoral offences tribunal which will be saddled with the responsibility of arrest, investigation and prosecution of offenders.”
Jega said that in the 2011 general elections, the commission detected 870,000 cases of multiple registrations out of the 73.5 million voters registered.
He, however, expressed regrets that only 270 offenders had been prosecuted by the body till date.
The chairman blamed poor funding and inadequate staff for the commission’s low performance in the prosecution of electoral offenders.
He said: “In INEC we have a very small legal department and for us to effectively have legal representation in cases of election petitions, we have to employ legal practitioners outside of that.
“We simply do not have the resources to prosecute; we have done our best but what we have done is just a drop in the ocean.”
On the November gubernatorial election in Anambra, Mr. Jega said the commission had set out modalities for continuous voter registration, adding that the prosecution of those caught in multiple registration had begun.
He promised that the modalities put in place by the commission would serve as a deterrent to people with the intention of indulging in multiple voter registration.
The INEC boss also said that continuous voter registration would be launched nationwide before the end of the year.
“We will prosecute offenders in each state but this will be done selectively because of the challenges of funding and the evidence that have been gathered by the police,” he said.
Jega said that the commission had set up a unit that would monitor campaign financing ahead of 215 elections.
“As we move towards 2015, we should have more effective monitoring of the use of money in politics,” he said.
Also speaking, Muthori Wangai, the Chairman, Independent Electoral and Boundaries Commission of Kenya, urged African countries to invest in institutions that would enhance the success of the electoral process.
Mr. Wangai said: “as we invest in the independent commissions, we invest also in the bodies that affect the electoral process and one of them is the judiciary and the judicial system in its entirety.
“It is important for us to think about improving the capacity to take action when the electoral system is abused.”
Another discussant, Francis Oke, from the ECOWAS Electoral Assistance Unit, urged African countries to invest more in the financing of elections and depend less on funds from foreign donors.