The TUV leader said he did not believe ex-prisoners should be jobless, but believed that restrictions should be placed on them becoming Stormont special advisers due to the "sensitivity of the position", on 12 December 2012.
Jim Allister was appearing before the finance committee to speak on his private member's bill.
It aims to ban those convicted of an offence carrying a sentence of five years, or more, from holding the senior role of special adviser.
He referred to previous evidence given by Sir George Quigley, the former chairman of the Ulster Bank, who had said he was worried the bill would be taken as a precedent to deny employment elsewhere.
"It's not being spread across the board. This bill is very precise and very focused on special advisers and it does not attempt to make it wider than that," Mr Allister said.
He also spoke on concerns raised by the Equality Commission that the bill would place a blanket ban on those applying for these positions.
"I refute the suggestion that it contains a blanket ban. It certainly is a very restrictive ban and it is certainly true that the ban is permanent and unreviewable," he said.
The North Antrim MLA also said there was a "misconception" that this bill was concerned only with terrorist convictions.
"This bill applies to anyone with criminal convictions of the magnitude of five years or more," he said.
Finance committee chairman Daithi McKay said some of those appearing before the committee had said it was worth considering that the government had given a commitment in the St Andrew's Agreement to work with businesses, trade unions and ex-prisoner groups to produce guidance for employers in the public and private sector.
Mr Allister responded saying he saw no "impediment in the Belfast Agreement, the St Andrew's Agreement or in the guidance from Sir George Quigley and others that prevents this bill from taking its course".
Mr Allister previously told the assembly he had brought forward the bill following the appointment of Mary McArdle as special adviser to Culture Minister Caral Ni Chuilin.
Ms McArdle's appointment stirred controversy in 2011 when it was revealed she had been convicted for her part in the IRA murder of Mary Travers in 1984.
The 22-year-old was shot dead by an IRA gang as she left Mass with her father, the magistrate Tom Travers.
Mr Allister said Mary's sister Ann Travers's evidence to the committee a number of weeks before had "clearly shown why the bill had been brought forward".
"You only had to sit and listen to Ann Travers to realise that, whether it was the 1980s, 1960s or 2000s, it is as raw today for victims as it ever was," he said.
Ms McArdle was sentenced to a life term for the murder and was released under the Good Friday Agreement.
Director of Personnel for the Northern Ireland Civil Service (NICS), Derek Baker, also addressed correspondence from Northern Ireland Association for the Care and Resettlement of Offenders (NIACRO).
He said the organisation that works with offenders to improve their welfare and prevent them from reoffending had raised three main concerns with the bill.
Mr Baker said that some of NIACRO's comments were based on a "misunderstanding of the processes we apply".
He said he refuted that the NICS did not apply the merit principle and stated that the civil service was the only part of the public sector that was subject to an external body in terms of recruitment.
He also said that those applicants found to have an unspent conviction would be written to and would be asked to make a statement of disclosure explaining the circumstances of the conviction, any mitigating circumstances, character reference and any evidence of rehabilitation.
Mr Baker said the individual would then be considered alongside the nature of the position.
The official also denied there was an absence of transparency within the NICS's recruitment process and said its policy and procedures manual was available on its website.