Mayor Phil Goff called the failures "not good enough" and demanded answers from KiwiRail and assurance it would not be an ongoing issue.
"We are promoting public transport, we are getting a big lift in the use of public transport - and therefore we need to be able to rely on it," Goff told the Herald.
"When you have two problems both relating to signals on KiwiRail infrastructure... we need an explanation and assurance this isn't going to be an ongoing problem."
Moyle said he had written to Goff to apologise.
"We take our role as manager of the network very seriously and we understand how important reliability is for commuters," he said.
He said KiwiRail had boosted its back-up power supplies to the signalling system following yesterday's failure by incorporating extra fail-safe elements.
This included back-up power supply systems with batteries and more generators to reduce the risk of future outages.
"In addition, we are initiating two reviews," Moyle said.
"An internal review has already begun, and an independent external review will be commissioned as soon as possible, covering all high risk failure points and, more importantly, what we need to do to prevent them happening in the future."
"We will discuss the outcome of those reviews with Mr Goff once they are complete."
Longer term, work is under way to create a new control centre for Auckland in the next 18 months and moving systems controls to a secure data centre, KiwiRail said.