A decision will be made in the next week about whether to continue with eradication or to move to containment. Until then, cows will continue to be culled.
No other country has managed to eradicate the disease, but officials were seeking further advice before making a decision.
Ardern confirmed that police had begun investigating the source of the outbreak.
"Obviously there's been a point at which this entered into New Zealand's borders and it has stemmed from there," she said.
"I do think we need to keep our options open over holding to account those who are ultimately responsible for the fact we are having to deal with this incursion in the first place."
The disease can cause pneumonia, arthritis and other serious conditions in cows, but it does not enter the food chain.
Ardern moved to allay any fears from consumers and importers, saying that it did not affect anyone who consumed it.
For that reason, the Government would not require farms to say if their products came from infected cows.
At last count, 38 farms have been found to be infected with the disease.
The acceleration of the disease's spread comes as farmers prepare for "Gypsy Day" on June 1, when sharemilkers move their cows to new farms.
The disease is heightened when stock are stressed, which meant the mass migration of cows around the country could worsen the situation.
The Prime Minister and Primary Industries Minister Damien O'Connor met farmers in Waikato, where a case of M. bovis was detected last week for the first time.
Ardern told farmers there the crisis had not yet reached the point where the Government response would change from eradication to containment.
"We're getting the best advice from around the world that we can.
"That's why we're working with industry to make some of those long-term decisions."
One of the key problems in managing M. bovis was the long and complicated testing process. Each test took 20 days and cows could sometimes produce one or two negative results before testing positive.