MEXICO CITY (Reuters) - Mexico is investigating a June shootout between the army and alleged gang members that killed 22 of the suspects, the attorney general's office said in a statement on Friday.

The gunfight took place on June 30 in Tlatlaya on the southern fringes of the State of Mexico, which borders Guerrero and Michoacan, states plagued by gang violence.

At the time, a spokesman for federal prosecutors said all the dead - 21 men and one woman - were believed to be gang members. The shooting started after soldiers came under fire from the suspected gang members, resulting in a gunfight lasting several minutes, the government said.

The case has come under closer scrutiny after a woman, who claims to have been a witness to the shootout, said in a magazine article the 22 people were executed after surrendering to the army.

"In relation to the events that took place on June 30, 2014 ... (the attorney general's office) affirms that there is an investigation into what took place," the statement from the attorney general's office said.

"A complete and thorough investigation is needed to get to the truth," it said.

In a separate statement, the army said it had every interest in a deep investigation and that it would cooperate completely.

"The army and air force are obliged to conduct themselves with the full respect for human rights," the statement said.

Mexican President Enrique Pena Nieto came to office in December 2012 pledging to quell gang violence that has killed more than 100,000 people since 2007.

Total homicides are down in Mexico since he took over but the death toll has risen in some places, like the State of Mexico - Pena Nieto's home state.

(Reporting by Gabriel Stargardter; Editing by Paul Tait)