Updated

The grisly discovery of mass graves in a Texas cemetery believed to contain the bodies of immigrants has raised questions about burial methods for bodies discovered along the U.S.-Mexican border.

The discovery was made at Sacred Heart Burial Park in the town of Falfurrias, about 79 miles north of the border, in the last two weeks. The multiple bodies -- so far there is no exact number -- were found by a team of students led by Baylor University anthropologist Lori Baker and Krista Latham, a forensic anthropologist at the University of Indianapolis, as part of a multi-year effort to identify immigrants who have died in the area near the border.

The team unearthed remains in trash bags, shopping bags, body bags or without a container at all, according to the Corpus Christi Caller Times.

In all, 110 unidentified people were exhumed from the cemetery in 2013. There have been another 52 graves found so far this summer, but because some remains were stored together, more work will be needed to determine exactly how many bodies have been recovered.

The finds have left state officials demanding answers.

“It’s an absolute disgrace and disrespectful,” State Representative Terry Canales, who represents the district in which Falfurrias is located, told FoxNews.com. “No matter what side of the borders they are from, these are human beings.

“It’s no excuse to disrespect someone in the way these bodies were.”

Canales added that he has filed a public information request to gain access to Brooks County’s expenditures to see how much was spent to bury the bodies and if anyone was acting improperly.

“It will give us a clear indication,” he said. “Without question there was some sort of fraudulent act.”

The Texas Department of Public Safety issued a statement late Monday saying, "The Texas Rangers discussed the situation with Brooks County officials today.  Another meeting is scheduled tomorrow in Austin with a variety of local and state officials to determine the proper course of action."

Researchers told the Caller Times that some remains were found under small, temporary grave markers bearing the name of a local funeral home -- Funeraria del Angel Howard-Williams.

Brooks County officials said they pay the funeral home to handle the bodies that are recovered in the remote parts of south Texas, a region that is often deadly for immigrants from Mexico and Central America who set out on foot amid sweltering temperatures to avoid Border Patrol checkpoints.

Over 300 people died crossing through Brooks County between 2011 and 2013 — representing more than half the deaths in Texas' sprawling Rio Grande Valley.

“The deaths of these individuals are tragic and difficult on many levels,” Jessica McDunn, a spokeswoman for Funeraria del Angel Howard-Williams told FoxNews.com. “For years now, Howard-Williams Funeral Home has worked closely with federal and local officials to handle these situations. We believe that all human remains should be handled with dignity, care and respect.”

McDunn added, “We applaud the efforts to identify next-of-kin and repatriate remains where possible. However, it is an unfortunate reality that some percentage of these remains will simply be unidentifiable despite the best efforts of the Medical Examiner’s Office and others.”

Howard Williams has maintained that while they have “certain records” related to the burials, they cannot confirm they were involved in the mass graves.

FoxNews.com’s Perry Chiaramonte and The Associated Press contributed reporting to this story.