WASHINGTON — A key Republican lawmaker wants to overhaul Social Security, the decades-old program that provides benefits to some 60 million retirees and disabled, with a plan to gradually increase the retirement age and slow the growth of benefits for higher-income workers.

Rep. Sam Johnson of Texas, the chairman of the House Ways and Means subcommittee on Social Security, introduced legislation just before the end of the congressional session last week that he said would “permanently save” the program. He said the bill would increase benefits for lower-income workers.

About 168 million people work and pay taxes toward the inevitable monthly Social Security benefits. About 42 million of the beneficiaries are retirees and their families. The trustees who oversee Social Security say it has enough money to pay full benefits until 2034, and then Social Security will collect only enough taxes to pay 79 percent of benefits.

Unless Congress acts, millions of people on fixed incomes would get an automatic 21 percent cut in benefits.

“Americans want, need, and deserve for us to finally come up with a solution to saving this important program,” Johnson said.