(CNN) The father of a 7-year-old Guatemalan girl who died after being detained by the US Customs and Border Patrol (CBP) said he has "no complaints about how Border Patrol agents treated him and his daughter," Guatemalan Consul Tekandi Paniagua told CNN on Saturday.

The consul said the father, Nery Gilberto Caal, told him agents did everything they possibly could to help his daughter, Jakelin Caal Maquin, after she became sick on a a bus. The bus traveled from the Antelope Wells port of entry in New Mexico to a Border Patrol station in Lordsburg, New Mexico, about 90 minutes away.

Caal did not speak to the media Saturday, but in a statement issued by his lawyers, he said he was "grateful for the many first responders that tried to save young Jakelin's life in New Mexico and Texas."

Still, his lawyers called for an investigation that "will assess this incident within nationally recognized standards for the arrest and custody of children. The family intends to assist in such an investigation into the cause and circumstances of Jakelin's death."

The lawyers, Enrique Moreno and Elena Esparza, also criticized border authorities for asking Caal to sign a form written in English about the state of his daughter's health not long after they arrived at the border, when she showed no problems.

But he speaks no English, the lawyers said. He speaks Q'eqchi', a Mayan language used in Guatemala, and Spanish is his second language.

"It is unacceptable for any government agency to have persons in custody sign documents in a language that they clearly do not understand," the statement said.

Jakelin had sufficient food and water, lawyers say

The lawyers clarified reports attributed to Homeland Security that Jakelin had "not eaten or had any water for several days" while crossing the desert before the border patrol took her into custody.

"Jakelin's father took care of Jakelin -- made sure she was fed and had sufficient water," the statement said. "She had not suffered from a lack of water or food prior to approaching the border."

The father has been staying at Annunciation House, a shelter for migrants in El Paso, since December 9, said Ruben Garcia, the Annunciation House director, at a news conference.

Jakelin's body was embalmed in El Paso and is on its way back to her village in rural Guatemala for burial, Garcia said. Friday afternoon, a prayer service was held and Caal "was able to spend time with her," he said. But he will not be able to leave to attend her funeral.

Garcia said he could not comment on Caal's legal status. The lawyers did not appear at the news conference.

Journey from Guatemala

The father and daughter lived with Jakelin's mother, Claudia Maquin, and three other children in the remote Mayan Q'eqchi' community of Raxruhá in the Alta Verapaz region of Guatemala.

Because of extreme poverty, Caal headed to the United States, taking Jakelin with him and leaving the rest of the family behind, Garcia said. The father and daughter traveled about a week before reaching the New Mexico border with a group of migrants the night of December 6 -- three days after her 7th birthday.

Nearly eight hours after they were detained, Jakelin and her father were loaded onto a bus bound for the Border Patrol station in Lordsburg, New Mexico, the CBP said.

Before leaving, her father told agents his daughter was sick and vomiting, the CBP said. An agent notified the station that the child would need emergency medical care.

When the bus arrived at the Lordsburg station at about 6:30 a.m., the father told agents the child was not breathing, according to CBP.

A Border Patrol EMT "revived the child twice," the agency said. She had a temperature of 105.7 degrees. Local EMTs also provided care before she was transported at 7:45 a.m. by air ambulance to Providence Children's Hospital in El Paso.

At 11 a.m. on December 7, officials at the Lordsburg station were notified the girl had again been revived after going into cardiac arrest, the CBP said. A CT scan revealed brain swelling. She was breathing by machine and diagnosed with liver failure.

Jakelin died at 12:35 a.m. Saturday, the CBP said. Her father was there.

The medical examiner has not said why Jakelin died.

"The El Paso County Officer of the Medical Examiner's office -- which conducted Jakelin's autopsy -- has made no public statement regarding her cause of death," the lawyers said in their statement. "In fact, neither the medical examiner nor Providence Children's Hospital have released records to Jakelin's father. We would ask that the media and federal agencies cease further speculation about her cause of death until these documents are released to Jakelin's family. Premature and inaccurate statements undermine the integrity of the investigation."

'Their lives are beyond impossible'

Speaking to reporters, Garcia said Caal reiterated that his daughter was fed and given water throughout the journey.

"The father told us, 'My daughter was eating. My daughter was receiving liquids and she was fine,'" Garcia said. "He's been very clear and consistent that his daughter was healthy and wanted to come with him."

Garcia said the father and daughter were not part of the well-publicized migrant caravan that traveled to the US border. They traveled by bus most of the way, he said.

When asked what he'd say to people who criticize the father for endangering his child, Garcia said the family lived in extreme poverty.

"Their lives are beyond impossible. None of us in the United States can imagine," he said.