Michael Flyger, a spokesman for New Zealand's health ministry, said latest figures showed that nearly 150 people have been reported sick, but he said the outbreak was not yet at "crisis point".
He told the Associated Press that it was "very, very unlikely" that the unknown flu strain had originated from the atolls.
"It's most likely a strain that has existed previously and has been brought onto the atolls by somebody returning or visiting," added Flyger.
Flyger said that being a small and isolated population, the inhabitants "tend to be what we call immunologically-naive, they don't get a lot of exposure to this sort of stuff so it can infect them a little more easily".
The first flu case was reported on March 16 and the outbreak had since spread to all three atolls, stretching the health resources of a few doctors and nurses "scattered around".
|Isolation has made the Tokulau islanders are vulnerable to infections [GALLO/GETTY]
New Zealand authorities have already sent a nurse, vaccinations and other medical supplies by boat from Samoa, and are expected to arrive by this weekend.
Fran McGrath, New Zealand's deputy director of public health, told Australian media that the government and the World Health Organisation had responded to residents' requests for medical assistance.
She said the response team will help to determine the source of outbreak and infection, as well as clinical and logistical support.
McGrath said Tokelau's isolated population does not have a high level of immunity to even the common flu or other viral conditions.
The three Tokelau atolls - Atafu, Fakaofu, Nukunonu - have no capital, airfield, sea port, cars or television.
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Tokelau's residents are New Zealand citizens who twice in recent UN-supervised votes have declined independence.