The new law passed in December gave prison authorities more power to keep dangerous inmates away from the public and allowed Corrections to apply for PPOs from the court for offenders with histories of serious violence or sexual offending.
Mr Key said internal reviews conducted by Corrections and the probation service had indicated they had done everything correctly in Robertson's case.
"We are not doubting that but we'll kick the tyres on that," he said.
When setting the terms of reference for the inquiry, the Cabinet would consider broader issues around the case and whether there were any further law changes "which at least could be contemplated", Mr Key said.
Asked if harder laws were a likely outcome of the inquiry, he said: "It's possible."
"In the first instance, I want Cabinet to consider the terms of reference on Monday, and then ultimately we'll let it do its work ... but most people would sit there aghast with what's taken place and obviously deeply frustrated."
Setting conditions around releases of offenders back into the community could be a difficult balancing act, he said.
"A lot of people are released and set about on a lawful life, but in this case, Mr Robertson hasn't and it's had disastrous consequences."
Earlier this week, Robertson lost name suppression, two months after being found guilty by a jury at the High Court at Auckland of the murder of Ms Gotingco.
Robertson is also a child sex offender and had just been released under the strictest possible conditions - including 10 years of GPS surveillance - when he killed her.
He was just 18 when he kidnapped and molested a 5-year-old girl in Tauranga in 2005.
Robertson was jailed in October 2006 for eight years after being found guilty of seven charges, including indecently assaulting the girl and attempting to abduct two other children.
On his release from prison in December 2013, he breached his conditions twice in a few weeks and was deemed such a lasting danger that he was to be monitored strictly for a decade, the maximum period of an "extended supervision order".
Robertson raped and murdered Mrs Gotingco three months after the supervision order was imposed but yet to be enforced.
Transport Minister Simon Bridges acted as Crown prosecutor in the 2005 case and sought preventive detention for Robertson - an unusual step for an offender who was still a teenager.
Mr Bridges, who was with Mr Key in Tauranga today for the opening of the city's new $445 million eastern link, isn't commenting on Robertson before he is sentenced next month.
