"I've handled it the best that I can," he said. "Obviously mistakes were made within the department. We've acknowledged that. The department has acknowledged that.
"As minister it's incumbent on me to review what happened and work with the department to assess where mistakes were made and where possible make changes."
The minister spent yesterday at Auckland Prison as part of his familiarisation with his new portfolio, before returning to Wellington for a briefing with officials.
He said he was first informed that Smith was on the run on Sunday afternoon, when Smith did not return to Springhill Prison as scheduled.
The minister called in the chief executive on Monday morning, and ordered an immediate review of the case.
Yesterday, Corrections suspended the temporary release programme until the policy could be reviewed. About 220 people a day are released from prisons on a temporary basis.
Corrections chief executive Ray Smith said inmates would only be released in exceptional circumstances during the two-week period, such as to attend a funeral. For any release, approval would have to be given by one of four regional commissioners.
"Public safety is paramount," Mr Lotu-Iiga said.
"We're intent that while the review's under way, we minimise the risk around this happening again."
Those on work-to-release programmes, where inmates work for a private company, would not be affected.
Escapes by prisoners on temporary release have been relatively rare. Corrections' annual report showed there had been none since 2009, when there were three cases.
Labour said Mr Lotu-Iiga had "serious questions" to answer over Smith's case.
Corrections spokeswoman Jacinda Ardern asked why Smith was not being monitored by GPS, which has been available to Corrections for tracking high-risk prisoners since August 2012.
Police Minister Michael Woodhouse said that would form part of the review.How did it happen?
How did it happen?
How was Phillip John Smith able to get a passport?
Smith was born Phillip John Traynor and had a passport issued to him in this name before he was imprisoned.
Internal Affairs does not have a list of alternative names for prisoners. That meant Smith could simply renew his old passport when it expired last year. All he had to do was provide an updated, verified photograph and fill out questions on the form.
Because the passport was in his birth name, it did not throw up any red flags at the Passports Office.
Internal Affairs Minister Peter Dunne says Smith clearly had help with the renewal form because it was submitted manually and was verified by a third party.
How did he have convictions in one name and a passport in another?
It remains a mystery why police charged him under the name Smith, especially because Internal Affairs revealed yesterday that he had never formally changed his name by deed poll. He is believed to have simply assumed the name later in life, and kept this name when he entered the criminal justice system. Smith's dual identities will be a key part of the police's review of the case. The Parole Board has previously warned of Smith's use of aliases.
What is the Government doing about it?
Internal affairs have cancelled Smith's passport. The department will look at why information is not shared between law enforcement agencies and the Passport Office, and why the department was not told about any name changes.
Corrections has suspended all temporary releases of prisoners. It is looking at why such a high-risk prisoner was allowed temporary release and also reviewing the broader policy of prisoner releases.