WASHINGTON — The Food and Drug Administration announced on Wednesday that it would require its toughest warning labels to caution patients against taking opioid painkillers together with benzodiazepines, like Xanax and Valium. The combination makes an overdose more likely and the warning is aimed at making sure people understand that.

Benzodiazepines are prescribed for anxiety, insomnia and seizures, and opioids for pain. The drugs work by depressing the central nervous system. Increasingly, doctors have been prescribing them together. The number of patients who were prescribed both drugs rose by 41 percent — about 2.5 million people — from 2002 to 2014, the agency said.

But the combination can result in extreme sleepiness, coma and death. The agency said a review of emergency room data in the United States showed that the overdose death rate involving both drugs tripled from 2004 to 2011. About a third of opioid overdose deaths in 2011 involved a benzodiazepine.