WASHINGTON — Federal health officials yesterday proposed sterner warning labels for acetaminophen, aspirin, and ibuprofen, again cautioning millions of Americans who take the nonprescription pain relievers regularly of potentially serious side effects.

The over-the-counter drugs remain safe and effective when used as directed, the Food and Drug Administration said. However, overdoses of acetaminophen can cause serious liver damage, even death, the FDA said.

For aspirin, ibuprofen, and other nonsteroidal anti-inflammatory drugs, there is a risk of gastrointestinal bleeding and kidney injury even when patients take the correct dose. The drug are linked to thousands of deaths a year. The FDA said the risk is rare when compared to the number of patients who take the drugs.

The drugs are found in hundreds of products sold to treat pain, headache, and fever. Health officials worry that the wide availability of those combination products allows patients to unwittingly overdose.

The FDA has updated the labels on the drugs multiple times in the past to warn patients of their risks. In 2004, some of the warnings contained in the new proposal were included in pharmacy brochures and public service ads — a move that some critics said at the time didn’t go far enough.

The latest proposed changes largely would beef up and highlight those warnings on the labels of the drugs. They also would require the more prominent disclosure — using fluorescent or bold-faced type — of the presence of the drugs among a medication’s ingredients.