By Edith Honan

NEW YORK, June 6 (Reuters) - Alishia Leitheiser has rescued animals since she was young, so the U.S. soldier's mother wasn't surprised to be picking up a stray dog from a U.S. airport on Friday that her daughter befriended in Iraq.

The black puppy with white legs and white spots -- named Iraqi by Leitheiser -- was one of 24 dogs flown from Baghdad to Newark International Airport in New Jersey this week by the Society for the Prevention of Cruelty to Animals International.

The dogs are set to be reunited with U.S. soldiers who adopted them.

"I was glad she had someone over there to give her hugs and kisses when her mom couldn't," Leitheiser's mother, Melissa Moore, told reporters at the airport as Iraqi stood at her side, wagging his tail.

Pets can play an invaluable role for U.S. soldiers in Iraq, helping reduce stress and promote emotional well-being -- even if interacting with stray animals is technically a violation of Army rules, the society said.

According to U.S. military data released in May, newly diagnosed cases of post-traumatic stress disorder among U.S. troops sent to Iraq and Afghanistan surged 46.4 percent in 2007, bringing the five-year total to nearly 40,000.

"While being over here, stress is dumped on each soldier every day, but when there is a piece of home somewhere nearby, it makes every day better," Leitheiser, a 20-year-old Army specialist from Felton, Pennsylvania, said in a statement. "Iraqi has been that piece of home for me."

The project's director, Terri Crisp, said that since Operation Baghdad Pups began last year, about 100 soldiers have e-mailed the organization for help adopting dogs and cats they befriended in Iraq and Afghanistan.

To qualify, puppies and kittens must have been found when they were less than 4 months old and not been part of a pack. They are given shots in Baghdad, followed by medical examinations once in the United States.

Crisp said the animals involved in the project are extremely well-socialized because soldiers have lavished them with attention from a very early age.

New Jersey State Assemblyman Neil Cohen, who teamed up with the Society for the Prevention of Cruelty to Animals on the project, said he has not lost sight of the big picture.

"If we had the power, I would be bringing (Iraqi) children and families here too," he said, as another Baghdad dog, Rocky, flipped onto her back, urging the assemblyman rub her belly.

Leitheiser and Iraqi will be reunited when her tour ends this summer. In the meantime, Iraqi will move in with Leitheiser's family, joining a hamster Leitheiser once rescued from a trash can and a cat she pulled from a gutter. (Editing by Michelle Nichols and Xavier Briand)

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