Up to 270 women in England may have died because they did not receive invitations to a final routine breast cancer screening, the Health Secretary Jeremy Hunt says.
Speaking in the Commons, he said 450,000 women aged 68-71 had failed to get invitations since 2009.
Hunt has announced an independent review and apologised "wholeheartedly" to the women and their families.
He said oversight of the NHS screening programme had "not been good enough".
Hunt told the Commons computer modelling suggested that between 135 and 270 women may have had their lives shortened.
GPs' leaders said they were "shocked" to learn of the error and said the implications for GPs would potentially be "significant".
Of the 450,000 women affected, 309,000 are still alive and in their 70s.
Hunt said: "For them and others it is incredibly upsetting to know that you did not receive an invitation for screening at the correct time and totally devastating to hear you may have lost or be about to lose a loved one because of administrative incompetence."
He said a computer algorithm failure was to blame, which meant, in some cases, women approaching their 71st birthday were not sent an invitation for a final breast scan as they should have been.
Variation in the way that local services sent out invitations may also have been a factor, he said.
Breast cancer screening is currently offered once every three years to women aged 50 to 70 in England.
All women affected will now be contacted by letter by the end of May and those under 72 will receive an appointment for a catch-up mammogram.
Women aged over 72 can contact a helpline to talk through the pros and cons of having breast screening - scans in older women sometimes pick up cancers which do not require treatment.
Any woman who wants a mammogram will get one within six months, Hunt said.
What to do if you're affected?
- Call the breast screening helpline number 0800 169 2692
- Go the NHS Choices website for more information
- You should receive a letter by the end of May
The health secretary said it was a priority to make sure additional scans did not cause any delays in the screening programme for other women.
Public Health England discovered the problem after analysing data and has apologised to the women affected.
Dr Jenny Harries, deputy medical director at PHE, said: "They and their families' wellbeing is our top priority and we are very sorry for these faults in the system."
Hunt told MPs in the Commons: "Irrespective of when the incident started, the fact is for many years oversight of our screening programme has not been good enough."
He apologised "wholeheartedly and unreservedly" for the suffering caused.
And he added: "We also need to get to the bottom of precisely how many people were affected, why it happened and most importantly how we can prevent it from ever happening again."
Women in Scotland are not affected by the error because it has a different IT system. Wales and Northern Ireland have similar systems to England but Hunt said there was no reason to believe they were affected.
The Royal College of GPs welcomed the independent review and urged women affected not to panic.
Prof Helen Stokes-Lampard, chair of the RCGP, said: "The priority should not be to establish blame, but to put measures in place to invite those women affected for screening, where appropriate; to ensure there are enough resources in the system to cope with any additional demand that might follow as a result; and to take steps to ensure this never happens again."
Emma Greenwood, Cancer Research UK's director of policy and public affairs, said the breast screening error was "very concerning".
She added: "It's worth remembering that many breast cancers are still found by women themselves, outside of the screening programme, so if you notice any unusual changes in your breast see your GP straight away."
Breast cancer screening is currently offered to women aged 50 to 70 in England.
All women in this age group registered with a GP are invited for screening every three years - around 2.5 million people.
This is because the likelihood of getting breast cancer increases with age.
After 70, women can still have screening if they choose to by contacting their GP.