WASHINGTON — The 60 million people on Social Security will not receive any cost-of-living increase in their benefits in 2016, the government said Thursday, but because of a quirk in federal law, nearly one-third of Medicare beneficiaries could have record increases in their premiums unless Congress intervenes.

With millions of older Americans on fixed incomes facing that one-two punch, the Obama administration is urging Congress to stop — or at least moderate — the health insurance premium increases, which could raise the cost for some Medicare beneficiaries by about 50 percent — the largest increase in the history of Medicare. But the leadership crisis in the House of Representatives could prove to be an obstacle.

Social Security has provided automatic cost-of-living adjustments in every year since 1975, with exceptions in 2010 and 2011. But inflation was extremely low in the past 12 months, leading to another benefit freeze, Social Security officials said. Gasoline prices, in particular, have declined sharply, holding down overall prices in the economy.

Jason Furman, the chairman of President Obama’s Council of Economic Advisers, has put a positive spin on the absence of a cost-of-living adjustment. It results, he said, from a “sharp decline in energy prices that is putting more money in families’ pockets” and is contributing to the economic recovery.