Story highlights Sgt. Andrew Tahmooressi says he accidentally crossed into Mexico on March 31

He had three weapons with him and was arrested in Mexico on a weapons charge

His mother and lawmakers are urging the State Department to get involved

Lawmakers have also written to the Mexican attorney general's office

For more than a month, a U.S. Marine and Afghanistan war veteran has been held in a Tijuana, Mexico, prison, fighting for his release after being charged with a crime he says he did not commit.

Sgt. Andrew Tahmooressi said he accidentally crossed into Mexico around 10 p.m. on March 31 with three personal firearms while on his way to meet friends in San Ysidro, California.

Tahmooressi, 25, had recently moved to the area to get treatment for his post-traumatic stress disorder and was "essentially living out of his truck," his mother, Jill, told CNN.

He is currently being held in the La Mesa penitentiary in Tijuana on a weapons charge and awaits a May 28 court date, according to the Mexican attorney general's office.

"I accidentally drove into Mexico with 3 guns ... a rifle (AR-15), a .45 cal pistol and a 12 gauge pump shotgun with no intensions (sic) on being in Mexico or being involved in any criminal activities," Tahmooressi wrote in a statement of innocence to U.S. Rep. Duncan Hunter. "I have rights to all 3 weapons. They are under my name ... Please help me."

Hunter, a California Republican, is among several lawmakers who have recently begun petitioning for Tahmooressi's release. Last week, Hunter wrote a letter to Secretary of State John Kerry, urging him to get involved.

Also, in a bipartisan congressional letter addressed to Mexico's attorney general on May 8, Hunter wrote:

"Mexico's Attorney General is in a position to deal with Andrew's case and ensure its quick resolution ... it is necessary that the AG intervene and expedite proceedings at the very least. And so far there's been no validation from Mexico that Andrew didn't make a directional mistake at the border."

The Mexican attorney general's office confirmed Tahmooressi's arrest on a weapons charge but could not offer more details about his case.

"Mother's Day is Sunday. If I can have my baby home on Sunday, that would be the greatest gift a mother could ever ask for," Jill Tahmooressi said in an interview from Miami.

"The brutality of being ... unjustly in a foreign prison is worse than any experience I had with him serving two tours in Afghanistan," she said. "He was willing to die for his country as a Marine. Where is his country now when he needs it the most?"

It is difficult for the U.S. State Department to quantify how many arrests are due to accidental crossings at the U.S.-Mexico border, a spokeswoman told CNN, but Andrew Tahmooressi's case is not all that unique.

In 2012, former Marine Jon Hammar was on his way to a surfing trip with friends when he was arrested while carrying an antique shotgun across the Mexican border checkpoint in Brownsville, Texas.

His mother told CNN that her son was arrested and held for more than three months even though he had registered his weapon with U.S. Customs and Border Protection agents before his trip.

"The press coverage led to his release," Olivia Hammar said in a phone interview. "It's an illegitimate (court) process (in Mexico). There's no oral arguments. You're guilty until you're proven innocent. Unfortunately, the only way to deal with that is ... if the (U.S.) State Department is not going to do something about it, then you have to go to the public and force them to do something about it. In our case, that's what moved things along."

In a daily press briefing this week, CNN asked State Department spokeswoman Jen Psaki about Tahmooressi's case, but she declined to comment, citing "privacy concerns."

Meanwhile, Tahmooressi's family is determined to secure his release.

In the weeks since his arrest, they have held rallies across the United States, done media interviews and promoted a whitehouse.gov petition to draw attention to his imprisonment.

"The affect (sic) of this unjust incarceration on a decorated combat Marine is despairing," the petition said.

As of Thursday evening, it had garnered nearly 12,500 signatures, about 87,500 short of the 100,000 required to get a response from the White House.