WASHINGTON  The government announced Thursday that it would sharply restrict some of the nation’s most popular prescription painkillers, saying they cause many patients to poison themselves with overdoses of the drug acetaminophen.

The decision by the Food and Drug Administration fell short of the ban on pills like Percocet and Vicodin recommended by an advisory panel in 2009. Instead, manufacturers of these drugs, which combine narcotics with acetaminophen, have three years to reformulate them or stop making them altogether.

Under the new limit, the pills may contain no more than 325 milligrams of acetaminophen  less than half the amount found in many of them now.

The action does not apply to over-the-counter pills like Extra Strength Tylenol, which also have more than 325 milligrams of acetaminophen and which the advisory panel also recommended banning. But more actions could be ahead, officials said.