Prime Minister John Key is backing his Corrections Minister and prison officials after the escape of a convicted killer.

At a press conference this morning, Mr Key said the Corrections Department had been "for the most part extremely well-run and highly efficient" in his time as Prime Minister.

He said the department would be reviewing Phillip John Smith's escape while on temporary release, and taking advice on whether a wider inquiry would be launched.

Corrections Minister Sam Lotu-Iiga is facing his first major test in the portfolio and Opposition parties say he has "serious questions" to answer about Smith's case.

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Mr Key said this morning: "I haven't seen anything from the minister yet that would indicate there are any issues."

He said it was not true that Mr Lotu-Iiga had kept a low profile since Smith's escape was revealed on Sunday.

"My understanding is that he's done a number of interviews."

As well as Mr Lotu-Iiga, Police Minister Michael Woodhouse and Internal Affairs Minister Peter Dunne have been handling Smith's escape.

Asked whether he would prefer Mr Lotu-Iiga took a lead role, Mr Key said he did not mind.

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Mr Lotu-Iiga has ordered an urgent review of Smith's case and his department has suspended all temporary releases of prisoners for at least two weeks.

The case has prompted concerns about how a high-risk prisoner was able to obtain a passport while in prison.

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Mr Key said there were "very valid" questions about whether enough information was transferred between government agencies.

Smith was able to flee the country by renewing an old passport which was under his birth name Traynor.

The passport renewal did not trigger any alerts at Internal Affairs because the name Traynor had a clean criminal record.

Police have been unable to explain why he was charged under the name Smith, which he has never officially adopted.

"All of this generates a series of different questions that need to be answered," Mr Key said.

Smith said in a statement to Radio New Zealand this morning that he fled because he had been a victim of a "vigilante justice system".

Mr Key said he suspected Smith was referring to the fact he was eligible for parole but had only been given temporary releases.

"That's his perspective, and there will be plenty of other people who have a different perspective."