"The public statements made by athletes who previously trained at the Karolyi Ranch are gut-wrenching," Abbott said in a letter calling for an investigation by the Texas Rangers into the facility in Huntsville, about 70 miles (113 km) north of Houston.
The facility has been used for regular training camps but USA Gymnastics said earlier this month it had canceled training sessions and was exploring alternative sites until a permanent location is found.
The complex was opened by celebrated gymnastics coaches Bela and Martha Karolyi in the mid 1980s and played a vital role in making the U.S. women's team a dominant force in global competitions.
Last week, disgraced longtime USA Gymnastics team doctor Larry Nassar, 54, was sentenced to up to 175 years in prison for abusing young female gymnasts who were entrusted to his care.
At his sentencing hearing in Michigan, about 160 of his victims gave harrowing accounts of the abuse they suffered at the hands of the Nassar, who served as the program's physician through four Olympic Games.
Victims also said some of the sexual abuse took place at the ranch.
(Reporting by Jon Herskovitz; Editing by Tom Brown)