Thinking about personal health at an early stage is vital to living a long and prosperous life, he said.
Public Health England (PHE) is stepping up efforts to improve provision and take-up of the checks.
A PHE review says checking 40 to 74-year-olds’ blood pressure, cholesterol, weight and lifestyle could identify problems earlier and prevent 650 deaths, 1,600 heart attacks and 4,000 cases of diabetes a year.
Before local authorities took over responsibility for commissioning the checks in April, there was considerable variation in how widely they were offered.
PHE, which leads the NHS Health Check programme, has launched a 10-point plan to help councils provide them to 20 per cent of their eligible local population a year – 15 million people by 2018/19.
PHE will also soon launch a website where it will be possible to show how many health check offers are being made by each authority.
Mr Hunt said: “Around 15 million people in England are eligible for a free NHS Health Check that could identify serious conditions early and add years to their life.
“I’d like to see all 40-74 year olds taking up this potentially life-saving opportunity.
“We could save 650 lives a year if there was full take-up.”