As pointed out by Reti, countries including Australia, Canada and the United States recommend screening up to 74 years of age.
"Extending the breast cancer screening age will mean that over a lifetime, the number of free mammograms a woman can have will increase from 18 to 20," Reti said.
"This will have the potential to save up to 65 lives per year."
October is breast cancer awareness month.
Grigg said among the most pressing concerns she heard from women were healthcare inequities.
"If the current Government does not make this change to save the lives of women across New Zealand, then a National Government will."
National Party leader Christopher Luxon, speaking to media alongside Grigg in Auckland today, said the change would enable about 240 women between 69 and 74 to access free mammograms.
He expected the extension would cost about $21 million. Luxon believed there were several current initiatives which funding could be redirected from to facilitate the change.
Asked about low screening rates for Asian women, Grigg said they would not introduce "race-based" policy and noted the change was about all women.
However, she did acknowledge Māori and Pasifika were more likely to die from breast cancer compared with Pākehā.