"If anyone feels they were disadvantaged by Ms Harrison during their employment at the Ministry of Transport I ask them to come forward so the matter can be investigated," Hughes said.
Meanwhile, Speaker David Carter has called a meeting with MPs this afternoon to discuss their concerns about Auditor-General Martin Matthews' handling of the case.
It comes after the Labour leader Andrew Little wrote to him earlier this week to ask for Matthews' appointment to be reviewed.
Carter told the Herald he had called together the seven-member Officers of Parliament select committee to discuss the issue. He could not comment further until after the 4pm meeting.
It comes after leaders of two Opposition parties refused to meet with Matthews.
Matthews is understood to have called party leaders yesterday to brief them about how he dealt with fraudulent activity by former Ministry of Transport senior manager Joanne Harrison when he was head of the ministry.
Labour leader Andrew Little and New Zealand First leader Winston Peters declined his offer.
Peters reiterated his call this morning for Matthews to stand down so the matter could be fully investigated, and said Prime Minister Bill English should intervene.
Peters alleged that Matthews' approach was instigated by the Government, which has distanced itself from the controversy surrounding the case.
"This smacks of the Beehive's involvement," he said.
English has repeatedly said it is not a matter for the Government because Matthews is a parliamentary appointment, and that any concerns should instead be raised with the Speaker David Carter.
Little wrote to Carter earlier this week to ask him to review Matthews' appointment.
Carter has been asked for comment.
Opposition parties who approved Matthews' appointment say they did not have the full details about his handling of the fraud case.
Harrison was jailed in February for three years and seven months for defrauding the ministry of $750,000.
Ministry staff had alerted Matthews to Harrison's unusual behaviour as early as 2013, but he did not act until April 2016, when he received a tip-off that Harrison had a criminal record.
Matthews said in a statement today that he regretted the events took place under his watch. He wished that he could have detected Harrison's criminal activity earlier.
But he stood by his decision-making, saying that it was based on the information he had at the time.
When he was notified about Harrison's history, he acted "swiftly and decisively", he said.
Since Harrison was convicted, former ministry staff members have claimed they were forced out of their jobs after raising concerns about her behaviour.
State Services Commissioner Peter Hughes is now considering an inquiry into the whistleblowers' allegations. He is expected to announce his decision this week.
Labour has also asked why Harrison got her job in the first place given she already had a fraud conviction in Australia - albeit under a different name.
