The Government is to reconsider the threshold at which hospitals must legally tell patients if they have been harmed, Health Secretary Jeremy Hunt has announced.
Ministers will consult on whether a new legal "duty of candour" should include all cases of harm to patients other than those at the lowest end of the scale.
The Government caused outrage last November when it said the duty of candour should mean patients and families are only told of harm if it results in death or severe disability.
The charity Action against Medical Accidents (AvMA) has campaigned on the issue, saying the vast majority of incidents which cause significant harm would not have been covered by the rule.
Hospitals would therefore not have been breaking the law in covering up such errors.
Under today's announcement, Mr Hunt has accepted recommendations from a report he commissioned on whether the legal duty of candour should also include cases of significant harm.
Professor Norman Williams, president of the Royal College of Surgeons, and Sir David Dalton, chief executive of Salford Royal Hospital, said it was in the interests of patients, families and providers of care that duty of candour applied to all harm not defined as "low".
In their report to Mr Hunt, they said the duty of candour should therefore also be applied to all cases of significant harm - covering moderate and severe harm, and errors resulting in death.
In a speech at the Virginia Mason Hospital in Seattle, Mr Hunt outlined plans to revise the threshold, force hospitals to apologise, and introduced other measures aimed at saving 6,000 lives over the next three years.
He said NHS organisations will be invited to "sign up to safety" and set out publicly their ambitious plans for reducing avoidable harm, such as medication errors, blood clots and bed sores.
If hospitals are successful in implementing them, the NHS Litigation Authority will allow them to reduce their premiums. Every year the NHS spends as much as £1.3 billion on litigation claims.
Other announcements include recruiting 5,000 NHS "safety champions" to identify unsafe care and fix it, and creating a new Safety Action for England team of doctors, managers and patients to provide intense support when things go wrong.
Patients will also be able to look at a dedicated section of the NHS Choices website from June called How Safe is my Hospital.This will enable comparison of hospitals in England across a range of patient safety indicators.
Mr Hunt said: "It is my clear ambition that the NHS should become the safest healthcare system anywhere in the world. I want the tragic events of Mid Staffs to become a turning point in the creation of a more open, compassionate and transparent culture within the NHS.
"We now have a once-in-a-generation opportunity to save lives and prevent avoidable harm - which will empower staff and save money that can be reinvested in patient care. Hospitals are already 'signing up to safety' as part of this new movement - and I hope all NHS organisations will soon join them."
AvMA chief executive Peter Walsh welcomed news the threshold on errors was being revised.
"This is potentially the biggest advance in patients' rights and patient safety since the creation of the NHS," he said.
"For decades, the NHS has frowned upon cover-ups but has been prepared to tolerate them. A lack of honesty when things go wrong adds insult to injury and causes unnecessary pain and suffering for everyone.
"Organisations that hide the truth are also less likely to learn from it. We are extremely grateful for the Secretary of State's preparedness to listen and the insight and leadership he has shown on this issue."
Shadow health minister Jamie Reed said: "The vast majority of NHS staff say David Cameron's NHS reorganisation is harming patient care. They warned him of the risks his reorganisation posed to the NHS, but he refused to listen and ploughed on regardless.
"The Tory-led Government is failing to learn the lessons of the Francis review - having handed out P45s to thousands of nurses and frontline staff. More than half of nurses now say their ward is dangerously understaffed, and more believe patient safety has got worse over the last year than better."
Dr Jennifer Dixon, chief executive of the charity the Health Foundation, said: "We welcome the commitment and ambition to improve patient safety demonstrated today by the Secretary of State and leaders of NHS providers.
"What really makes a difference is frontline organisations having the space and resources they need to set their own goals, motivate staff and skill them up to deliver better care for patients.
"It is challenging but crucial to get the balance right between top down direction and bottom up engagement. To accelerate progress, policymakers should give as much attention to enabling frontline organisations to understand and improve the quality of their services as they do to scrutinising them."
Cathy Warwick, chief executive of the Royal College of midwives, said: "The safety of the people in our care should be at the centre of everything that the NHS does, and our NHS is one of the safest health services in the world. However, I worry that I have heard this before from Governments without any real progress being made.
"Safety is about having the right numbers of staff and high-performing teams working together to deliver the best care, and this is crucial if we are to deliver safe maternity care.
"Safety also needs NHS staff being treated properly with trusts promoting open, honest and caring cultures if they are to get the best out of them; you can only have candour if staff feel their concerns will be listened to, they are treated with compassion and that they will be given the support they need."