ATLANTA — After falling four years in a row, U.S. births may finally be leveling off. The number of babies born last year — a little shy of 4 million — is only a few hundred less than the number in 2011, according to a government report released today.

That suggests that lately, fewer couples may be scared away from having children because of the economy or other factors, some experts say. Among the signs of a possible turning point: The birth rate for women in their early 30s inched up for the first time since 2007.

“We may be on level course or potentially even see a rise” in birth trends in the near future, said Brady Hamilton, a statistician with the Centers for Disease Control and Prevention.

Some are a bit more pessimistic.

“The decline has slowed down, but it’s still a decline,” said Carol Hogue, an Emory University expert on birth trends.

Falling births is a relatively new phenomenon in this country. Births were on the rise since the late 1990s and hit an all-time high of more than 4.3 million in 2007. The drop that followed was widely attributed to the nation’s flagging economy. Experts believed that many women or couples who were out of work or had other money problems felt they couldn’t afford to start or add to their family.

The economy officially was in a recession from December 2007 until June 2009. But well into 2011, polls showed most Americans remained gloomy about the economy.

The new CDC report is a first glimpse at 2012 birth certificate data, but the numbers aren’t expected to change much.

Highlights include:

• The birth rate for all women of childbearing age — 63 births per 1,000 women — was essentially flat from the year before.

• Rates fell again for women in their early 20s, down 3 percent from 2011.

• For women in their late 20s, birth rates fell 1 percent. The rate rose a slight 1 percent for women in their early 30s.