"However, the minister would consider any advice that would improve the bill," a spokeswoman said.
In the meantime, Corrections was expected to begin an inquiry into Robertson's offending tomorrow, which would review his electronic monitoring conditions.
Labour MP Kelvin Davis was unsure whether Labour would back the bill when it returned to Parliament.
But he said the high rate of people breaching their electronic monitoring conditions "should be ringing alarm bells" and the policy of using GPS monitoring for ex-offenders in the community needed to be reviewed.
New Zealand First corrections spokesman Mahesh Bindra said he still supported the expansion of GPS tracking, but he wanted additional safeguards to be built into the law.
Electronic monitoring was introduced in 2006 for people on home or community detention, and was extended to some high-risk criminals in 2012.
The new bill, which is at the select committee stage, would expand the policy to two new sentences.
These were prison sentences of up to two years which had release conditions, and intensive supervision sentences.
At the first reading of the bill, Mr Lotu-Iiga said offenders in these categories had a higher likelihood of reoffending, in particular stalkers.
Labour supported the bill to the select committee stage, where it could be determined whether or not the measures went too far or not far enough.
There are currently around 3500 people being electronically monitored in the community.
Of the 238 people on extended supervision orders (ESOs) - which required high-risk offenders to be monitored at all hours by GPS technology - seven breached their conditions in the 2013/14 year. Robertson was on an ESO when he killed Blessie Gotingco last year.
Mr Davis said the worst offenders needed to have an "instant action" classification, "so when their alarms are triggered there is no mucking about".
Police defended their response to the Livingstone case, saying that they did not have a warrant to enter his house after his anklet alarm was set off.
Livingstone's house was not entered until seven hours after a "tamper alert" was triggered.
Who can be electronically monitored?
NOW: People on home detention, community detention, extended supervision orders, parole, release-to-work schemes, or those who have been bailed with specific conditions.
PROPOSED: Offenders with "intensive supervision" conditions and people serving prison sentences under 2 years which have release conditions