No district in Auckland had a higher resolution rate than 10 per cent. Mr Goff said these statistics provided no incentives for criminals to stop offending.
Mr Woodhouse agreed that the resolution rate was "concerningly low".
"I have communicated those concerns to the commissioner and asked him to advise and plan for efforts to increase the resolution rate of minor crime," he said.
The minister said minor crimes had the potential to erode trust and confidence in police.
"I think it's something New Zealand police need to focus on, to continue to focus on," he said.
Police were already making renewed efforts on minor crimes, such as a recent push to crack down on car theft in Counties Manukau.
"That's a very good practical example of where police see a specific issue in a district and respond to it," Mr Woodhouse said.
Mr Goff asked why police funding had been reduced in the Budget when burglary rates were rising and resolution rates were falling.
He said crime case resolution had been trimmed by $1.7 million and criminal investigations had been cut by $1.2 million.
Mr Woodhouse said resources were increasingly being shifted from investigation to prevention, and that had helped reduce crime in many areas.
He did not accept that this shift in resources had contributed to the fall in resolution rates.
"I'm confident that the police continue to have the resources they need to increase the resolution rates and that's what I'm asking the commissioner to work on."
Mr Bush told the committee he was also concerned about the resolution rate for minor crimes.
"We need more focus on burglaries, we absolutely agree with that, car crime [in particular] is something that is very difficult to resolve."
He said authorities around the world had struggled to raise resolution rates for car theft, and the best New Zealand could hope for was around 10 per cent.
If funding was redirected to deal with investigating the large number of car thefts, it could lead to a drop in prevention, he said.
Mr Bush also told the committee that the falling resolution rate was partly due to a recent redefinition of burglary within the justice system.
He said that if someone had a gnome stolen from their front yard, that was now classed as burglary.
"That in previous years would not be considered a burglary."
According to the Police Association, the police budget this year fell by 1 per cent, from 1.624 billion to 1.609 billion.
