PIEDRAS NEGRAS, Mexico — Officials said Tuesday they have found three inmates thought to have escaped through a tunnel at a northern Mexico border prison, lowering the number of escaped prisoners to 129.

Three female inmates were found hiding in a prison visiting area, said Jorge Moran, the public safety secretary of the border state of Coahuila.

Federal police units and Mexican troops, including 70 members of an elite military special forces unit, are searching for inmates who fled the prison in Piedras Negras, a city across the border from Eagle Pass, Texas.

They escaped Monday through a tunnel 21 feet long and 4 feet in diameter, then cut their way through a chain-link barrier and escaped onto a neighboring property.

The director and two other employees of the state prison have been detained for an investigation, and President Felipe Calderon called the jailbreak “deplorable” Tuesday.

Calderon appeared to re-ignite the long-running dispute between federal and state authorities, writing on his Twitter account that “the vulnerability of state law enforcement institutions must be corrected.”

Collusion between guards and drug gangs has played a role in past escapes, and federal authorities have been pushing to have all state and municipal police and law enforcement officials submit to background and anti-drug checks, as well as vetting for possible links to organized crime.

State authorities have been dragging their feet. On Monday, federal Interior Secretary Alejandro Poire said that 180,000 of the country’s 430,000 city and state police have been vetted and checked, and that about 65,000 of those tested had failed the tests.

Only 12 guards were on duty to watch 734 inmates, Moran said, after some guards and officials were dismissed after failing background checks.

In February, nine guards at a prison near the northern city of Monterrey confessed to helping 30 Zetas drug gangsters escape.