Liberal Democrat leader Willie Rennie demanded the minister go before MSPs after figures leaked to The Herald's sister paper, the Sunday Herald, showed 550 civilian staff would be lost immediately.
The single force's newly appointed chief constable, Stephen House, said last week the merger could mean up to 3000 civilian jobs could be lost.
The Sunday Herald reported a leaked document containing figures from the Police Reform Board shows the force faces £300 million-worth of cuts over the next three-and-a-half years.
The document also shows plans for further job cuts in future years, with cash set aside for redundancy and early retirement costs, the newspaper said.Speaking on BBC Scotland's Sunday Politics programme, Chief Superintendent David O'Connor, president of the Association of Scottish Police Superintendents (ASPS), said he does not recognise the figures.
The Liberal Democrats were opposed to the legislation passed by Holyrood, which allowed the merger to go forward.
Commenting on the Sunday Herald report, Mr Rennie said: "These cuts are even worse than we feared. The costly upheaval of centralising our local police forces will have a big impact on their effectiveness.
"The Justice Secretary must come before Parliament to explain himself."
Mr O'Connor said the figures quoted in the Sunday Herald have not been discussed by the police reform group.
"As a member of that group, I haven't had an opportunity to scrutinise these figures," he said. "The new policing model for Scotland must comprise police officers and police staff, and obviously we would like to have an early meeting with Mr House and the convener of the new Scottish Police Authority."
ASPS has always supported the concept of a single police force, and one of the reasons is the maintenance of police officer numbers, he said.
A Scottish Government spokesman said: "We have protected, and will continue to protect, frontline police numbers and the 1000 extra officers we have delivered, which have helped reduce crime to a 37-year low. We have also given a commitment to no compulsory redundancies among police support staff.
"The new service will eliminate duplication, saving £1.7 billion over 15 years and supporting a single chief constable and one senior management team."
The single police force is expected to go into operation in April next year.