The number of preterm births in the United States increased by more than a third between 1996 and 2004, and Cesarean sections accounted for the vast majority of the increase, researchers said Wednesday.

Most of the increase involved what physicians call late-preterm babies, those born after 34 to 36 weeks of gestation rather than the normal full term of 38 to 42 weeks.

Physicians are concerned about the growing number of late-preterm babies – which now account for 72 percent of all preemies – because recent studies have shown serious health risks for them, including immature organs, breathing problems, feeding problems, difficulties regulating body temperature, jaundice and a three-fold increase in death during the first year of life.

The number of deaths is small, about three per 1,000 late-preterm births. “But it is a serious problem,” said Dr. Alan R. Fleischman, medical director of the March of Dimes.

Many of the other problems eventually resolve themselves, but cost of the added care can be substantial.

According to the Institute of Medicine, medical costs associated with premature delivery total $26 billion per year in this country. More than 50 percent of those costs are for complications involving late-preterm babies, Fleischman said.

While many C-sections are medically necessary, experts fear growing numbers are the result of physicians’ fears of lawsuits arising from complications during labor and the mothers’ desire to schedule the births at a convenient time.

The American College of Obstetrics and Gynecologists has guidelines firmly stating that C-sections should not be performed unless there are medical indications for it.