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."
This week Robertson lost name suppression, two months after being found guilty by a High Court jury of the murder of Mrs 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 18 when he kidnapped and molested a 5-year-old girl in Tauranga in 2005. He was jailed for eight years.
On his release from prison in December 2013, he breached his conditions twice in a few weeks and was deemed such a lasting danger he was to be monitored strictly for a decade, the maximum period of an extended order.
Robertson raped and murdered Mrs Gotingco three months after the supervision order was imposed but yet to be enforced.
On Wednesday, Corrections Minister Peseta Sam Lotu-Iiga announced an independent review of Corrections' monitoring of Robertson after his release from prison.
Mr Lotu-Iiga was seeking advice on what form the review would take and planned to discuss it at Monday's Cabinet meeting. He earlier said he was confident Corrections had done all it could and indicated the new powers now in place could have kept Robertson away from the public.
