The number of children being hospitalized because of prescription opioid poisoning has risen sharply since 1997, especially among toddlers and older teenagers, researchers from Yale School of Medicine report.

The study, published Monday in JAMA Pediatrics, analyzed data from the Kids’ Inpatient Database, a national database of pediatric hospitalizations. Looking at data gathered every three years from 1997 through 2012, they identified 13,052 instances in which children and teens ages 1 to 19 had been hospitalized for prescription opioid poisonings; 176 of them had died.

Among children ages 1 to 4, hospitalizations for opioid poisoning increased by 205 percent. For teens 15 to 19, hospitalizations rose by 161 percent.

Children ages 1 to 4 were primarily hospitalized for accidentally ingesting opioids, while the majority of teens over 15 took the drugs with the intent to commit suicide, said Julie R. Gaither, the study’s lead author and an epidemiologist and postdoctoral fellow at Yale. She said other teenagers probably overdosed when taking the drugs for recreational purposes. She attributed the increase in poisonings among toddlers to parents or other adults within the household leaving pills within easy reach of young children.

Dr. Gaither said poisonings attributed to prescription opioids are now the leading cause of “injury-related mortality” in the United States, largely because of the wider use of the drugs in households nationwide. In 2012, doctors wrote 259 million prescriptions for opioid painkillers.

“The medical community needs to develop a safety plan for parents to store the pills and make their homes safe for their children,” Dr. Gaither said. “Physicians prescribing medications to an adult, or even a teen, need to ask if there are younger kids in the household and, if so, to make sure they know how potent the drugs are and to keep them out of reach of kids.”

Dr. Gaither said the pills should be more securely packaged and better labeled.

“Oftentimes, parents are not told what to do with leftover medication, and that means it is left sitting around your house where your kids can find them,” said Sarah Clark, co-director of the C.S. Mott Children’s Hospital National Poll on Children’s Health.

In a C.S. Mott poll earlier this year of nearly 1,200 parents with at least one child between 5 and 17, about one-third of parents said their children had been given prescriptions for opioids, and nearly half had leftover medication. Only 8 percent said they returned the unused medication to a pharmacy or doctor. Forty-seven percent kept the leftover drugs at home; 30 percent threw them in the trash or flushed them down the toilet; 6 percent said other family members used the leftover medication and 9 percent did not remember what they did with the rest of the medication.

“Most doctors don’t talk about the dangers of opioids and children,” Ms. Clark said. “We are really leaving it up to the parents’ initiative to solve this problem, and most parents are not medical experts. I would love to see the health care community step up and say let’s be more proactive about dealing with leftover medication.”

Jen Simon, a freelance writer in the New York City area who has written about her addiction to painkillers, said she had never been told how to dispose of leftover prescription medication, and her doctors had never cautioned her about the dangers of opioids if ingested by her two young children.

“And my doctors know I have young children — they have been to my medical appointments with me,” Ms. Simon said.

Dr. Richard N. Rosenthal, a professor of psychiatry and an addiction psychiatrist at the Icahn School of Medicine at Mount Sinai in New York, said doctors need to be properly trained on how to counsel patients who are being prescribed opioids on all aspects, including proper disposal of leftover medication.

“Opioids can be a ticking time bomb in your medicine cabinet,” Dr. Rosenthal said, adding that overprescribing of medications also must be addressed.

“Doctors should only prescribe what is necessary to take care of short-term acute pain,” he said. “You can always go back to your doctor if you feel you need more, but you should not take home more pills than needed.”