Los Angeles (AFP) - A girl abducted by her mother over 12 years ago was reunited with her father Wednesday after being found safe and well in Mexico following a joint US-Mexican rescue operation, investigators said.

Sabrina Allen went missing in 2002 at the age of four, and was rescued in the operation Tuesday in the town of Estafeta Tlaxcala, some 90 miles (140 kilometers) east of Mexico City.

She is now 17 years old. The Federal Bureau of Investigation (FBI) said her mother evaded arrest for so long by fleeing the country, moving frequently and constantly taking on new identities.

The mother, 44-year-old Dara Marie Llorens, also frequently changed the girl's hair color, according to media reports.

"I am overjoyed that Sabrina has been found alive and is safe," said her father Greg Allen, who appeared at an emotional press conference in Austin, Texas.

"Our entire family would like to thank the investigators that made this happen," he added in a statement released by private eye firm Klein Investigations and Consulting, who helped track down his daughter.

He had been given sole custody of his daughter when he divorced his wife in 2000. But she "knowingly abducted" the child during a weekend visit in April 2002, according to an affidavit.

One Mexican police officer was injured in Tuesday's operation to rescue the girl, officials said, adding that both Allen and her mother were returned to the United States overnight.

The father added: "Our prayers go out to the Mexican Federal Police officer who was injured. We also would like to thank the Mexican government for their cooperation in this case.

"They never gave up," he said, also thanking the Federal Bureau of Investigation and US marshals who took part in the mission.

The FBI said that for more than 12 years, "working with law enforcement agencies throughout the world, (it) conducted proactive investigation and followed up on hundreds of leads and tips regarding Llorens’ whereabouts."

But "by assuming new identities and moving frequently throughout the years, Llorens was able to narrowly evade capture on more than one occasion," it added in a statement.

It added that following the mother's arrest Tuesday, "the child was safely recovered in Mexico and reunited today (Wednesday) with her father in the United States."

The teenager is undergoing medical and psychological counselling at an undisclosed location, while her mother is in custody pending action for aggravated kidnapping, according to the affidavit.

The rescue team's leader, Phillip Klein, said emotions ran high as they finally found mother and daughter Tuesday.

"There were a lot of tears last night on many sides," he told local TV affiliate Fox7 news. "Our team was emotional ... I think the emotions finally let loose last night."

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