WASHINGTON — When it comes to the risks of identity theft, the U.S. government isn’t taking its own advice.

The nation’s Medicare agency and the Pentagon compel at least 52 million Americans to carry their Social Security numbers in their wallets, contrary to warnings by the Federal Trade Commission that people should avoid doing so.

At least 44 million Medicare insurance cards include the beneficiary’s full Social Security number.

Social Security numbers also appear on 8 million Defense Department identity cards used by active duty and reserve forces and their dependents, and on identification cards issued to military retirees. The Pentagon plans to remove the numbers but won’t complete the effort until 2014.

And the Internal Revenue Service still tells taxpayers to write their Social Security number on checks used to make payments, a potential problem for those using the mail rather than filing electronically.

All this contradicts advice from the Federal Trade Commission, the lead federal agency for deterring identity theft.

“Protect your Social Security number. Don’t carry your Social Security card in your wallet or write your Social Security number on a check,” the FTC warned in a pamphlet sent months ago to every mailing address in the United States. The Social Security Administration offers similar advice.

Carrying a Medicare card with the full Social Security number is more of a problem than the Social Security card. People usually need the insurance card to visit a medical provider but can memorize their number and always leave their Social Security card at home.

The Centers for Medicare and Medicaid said it would be too expensive for the agency, and for medical providers linked to Medicare, to change their systems with new numbers. Medicare officials also said they know of no cases in which identity theft was traced directly to a lost or stolen Medicare card.