The Government was still falling short on contact tracing targets a week ago - 10 days into the current COVID outbreak.
But it says the data is skewed by early cases and the next batch will look better.
It released several new sets of tracing data, covering the first 10 days of the current outbreak, along with a long-awaited report into progress on improving the country's contact tracing system.
The new data showed that the several targets for getting people with COVID - and their contacts - into isolation or quarantine quickly fell well short of being fast enough.
One target called for 80 percent of contacts to be in isolation within four days of a case's first symptoms, but that was only at 37 percent.
Director of public health Caroline McElnay said the data was skewed by the very start of the outbreak, so by the time people were found to have COVID, they had already been infected for several days.
It did show contact tracing teams were exceeding the gold standard in the time taken to find an infected person's contacts - 80 percent of contacts in 48 hours. That meant those contacts could get into isolation and get tested, lessening their chance of spreading the disease.
Mathematician and COVID modeller Michael Plank said contact tracing had been made a lot easier because the country was at level 3. Level 2 would put the system under a lot more stress.
"People start to move around more, they start to have more contact, they're back into their work places... it's a real unknown as to how the contact tracing system will perform in that environment," he said
Epidemiologist Nick Wilson said speed was very important when trying to keep an outbreak in check.
"Although there has been some good improvements over time, and definitely better than March and April, there is still away to go," he said
A report led by Sir Brian Roche into contact tracing that was released yesterday also said the contact tracing system had improved.
But it highlighted problems with the fragmented nature of the health system, including public health units often acting independently.
It alluded to the confusion surrounding the testing of border workers, saying there needed to be more clarity on the command and control structure of the COVID response.
Prof Wilson said while all those points were valid, the report - which was given to the Government six weeks ago - was now old and had big gaps.
Its scope was too narrow and it should have focused more on technology, he said.
The Roche report did acknowledge the need for better tech, warning that the COVID Tracer app would be much less effective when alert levels were low and people became complacent.
It said the Government should consider smartphone and bluetooth technology for easy tracing.
But Prof Wilson said harnessing phone data should be one of the top priorities, rather than the report's focus on problems with the health system which were harder to change.
"It just seems crazy that Google and Apple know where I am all the time when I'm a carrying a smart phone but the Government is not allowed to know where I am even in a public health emergency where it's potentially going to save a lot of lives," he said.
The Ministry of Health said it was looking at trialling the Apple and Google systems but it would take time to make it work with the current system.
It said the bluetooth CovidCard would be trialled in Rotorua next month.
Health Minister Chris Hipkins said the contact tracing system had improved even since Sir Brian's report and different parts of the health system were now working much better together.