Around $703 million in wage subsidies had been repaid voluntarily by March 5, the report said, with a further $23m "compulsorily recovered".
On Tuesday the Auditor-General released its report into the management of the scheme, which found that while it was mainly well managed, more checks were needed.
"Because this approach has greater risks of fraud and error, strong post-payment checks are vital to verify that those who received money were eligible," Ryan said in a statement.
While the publishing of the names of businesses which received the subsidy probably led to a number of employers repaying, Ryan criticised the work MSD did to test whether employers were complying with the rules.
"After payment, MSD's reviews mainly consisted of a verbal confirmation of information by employers," Ryan wrote.
"Although the Ministry of Social Development has publicly described these reviews as audits, in my view they are not audits. In most cases, they did not involve substantiating the facts using independent, or at least documented, information," Ryan wrote.
"I am not persuaded that the reviews provide enough confidence that all applications that merit further investigation have been identified. As at 5 March 2021, 1017 cases had been referred for investigation."
Ryan has recommended that MSD test a sample of the reviews against documentary evidence held by the applicants.
"In my view, the use of a high-trust approach at the outset needs to be balanced with adequate verification after the payment has been made to properly protect the use of public money."
He also recommended MSD "seek written confirmation from applicants of their compliance with the eligibility criteria and the obligations of receiving the subsidy".
The departments which managed the scheme had identified "a number" of applicants that they considered might have acted unlawfully.
"In my view, it is important to pursue prosecutions of these applicants. This is because it is important to maintain public trust and confidence in government schemes."
'Exceptional hours'
While the report made pointed remarks about investigating the scheme's problems, the Auditor-General heaped praise on the departments which managed the scheme, especially MSD, given the time they had to set it up.
The Auditor-General pointed out that the Government only decided that MSD would administer the scheme two days before the first applications were submitted. It was preferred over Inland Revenue, which had the capability to administer the scheme, but was approaching a busy time in the tax-filing cycle.
"In our view, public organisations involved in administering the scheme worked well together under challenging circumstances and time frames. This included consulting effectively about important decisions and connecting staff from the Ministry of Social Development with Inland Revenue to appropriately share information."
Ryan said the "goodwill" of public servants was essential for the delivery of the scheme, saying some worked "exceptional hours in very difficult circumstances" to establish the scheme and process applications.
"They also had to deal with distressed people who were facing losing their businesses and/or livelihoods."
The scheme required heavy resource, with up to 800 people working on it on a busy day.
Resourcing the scheme took resource away from other parts of MSD, including putting some investigations into benefit fraud on hold.
Organisations involved in the scheme were unable to work out how much it had cost to administer.
