Councillor Bhupendra Patel, 61, had pleaded guilty to the offence of failing to disclose his councillor allowance while receiving incapacity benefit.
He failed to promptly notify the Department for Work and Pensions of a change of circumstances that affected his entitlement to state-funded incapacity benefit, which involved his earnings as a councillor.
Last week, Patel was sentenced to eight weeks in prison, suspended for a year, and ordered to pay 85 pounds costs to the Crown Prosecution Service.
"All I did was misinterpret the law. I did not commit fraud...I overlooked something," Patel told the 'Northampton Herald and Post'.
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"I have been elected to Wellingborough Council until 2015 and Northamptonshire County Council until 2017. In terms of the councils I have done nothing wrong and have abided by their rules and regulations...I was elected to the council to represent the community and this is what I will do," he added.
Wellingborough Council chief executive John Campbell has admitted that under the Local Government Act 1972 the conviction of a councillor, which results in a prison sentence of less than three months, does not disqualify them from being a member of a borough council.
"As leader of the council, I strongly condemn the actions of Bhupendra Patel and call on him to resign with immediate effect," he said.
"Clearly Bhupendra Patel has breached that trust and confidence, and I can't see how he can continue as a councillor...There is no excuse for benefit fraud and someone holding public office and responsible for public money knows that as much as anyone. I am appalled that we find ourselves in this situation," Bell added.
Patel has represented the town's Hemmingwell ward since 2003 and was mayor of Wellingborough in 2011-12.