It sought data on issues suffered by the children and also mothers during conception and child birth.
"It is hoped the results will establish the truth of the genetic transfer of illnesses related to the nuclear exposure encountered by the crews that were sent to Muruoa Atoll in 1973," said Mr O'Donnell.
Since the group formed two years ago, he said it had met Veterans Affairs Minister Craig Foss and senior officials and more communication was expected from both sides.
In response to New Zealand Herald questions, the minister said the Government would consider assisting research into the health of Mururoa veterans and their descendants, if such a study was proven to be warranted.
The minister said that at the end of June, 93 veterans who served at Mururoa were receiving a War Disablement Pension, under the Veterans' Support Act.
A list of "conclusively presumed conditions" supported veterans of Pacific testing.
A veteran diagnosed with a disability on the list was entitled to free medical treatment.
The ministry said available evidence was that Mururoa veterans were not exposed to harmful doses of ionising radiation in the frigates, neither of which came within 20 nautical miles of a test detonation -- the minimum safe distance.
The French Government's subsequent move to underground testing was cause for veterans to celebrate a successful mission, instead of raising alarm about unproven health risks, says naval historian and author, Gerry Wright, who was the Otago's operations officer.
In his latest book on the protest, Operation Pilaster, Mr Wright said the ships' crews were "no more likely to experience cancers or any other radiation causing illnesses than anyone else".
He had studied reports of the National Radiation Laboratory's monitoring on both frigates.
"The radiation exposure to both ships' crews from fall out was essentially zero."
He knew first-hand that the frigates were well prepared to protect crews from contamination.
"I've written this book because people are concerned ..children are concerned what their fathers went through.
"I'm saying calm down; you didn't have to go to Mururoa to get cancer."
Mururoa protest by the numbers
•1973 Government tackles France on atmospheric nuclear tests
•2 Navy frigates sent to Mururoa Atoll
•500 total crew served
•2 bomb explosions witnessed from 20 nautical miles out to sea
•1975 French Government moved to underground testing.
•93 Mururoa veterans get War Disablement Pension
