MANCHESTER, N.H.—Gov. Chris Christie called for reduced Social Security benefits for retired seniors earning more than $80,000 and eliminating the benefit entirely for individuals making $200,000 and up in other income, along with raising the retirement age to 69 from 67.

The changes would not apply to current retirees or those near retirement, but could help keep Social Security sustainable for future generations, Mr. Christie said. Not acting would jeopardize longevity of Social Security and other entitlement programs, he said, and potentially lead to massive tax increases to prop them up.

“Every other national priority will be sacrificed, our economic growth will grind to a complete halt and our national security will be put at even graver risk,” Mr. Christie said during a 40-minute speech Tuesday.

Mr. Christie’s decision to take on Social Security, Medicaid, Medicare and disability insurance stands as perhaps the most significant policy proposal to date in the 2016 race, and one that will likely result in attacks from Democrats and his potential Republican competitors.

While national Republicans have often highlighted the need to scale back on health care entitlements, Social Security has presented more of a political third rail.