The four undocumented migrants had been dead a week to nine days when they were found Dec. 13 in their apartment in the Cincinnati suburb of Sharonville.
Two of the victims left behind a wife and two children each, said Filemon Guardado, a second cousin of all four victims, speaking to The Associated Press by telephone.
"They were very hardworking. They did not deserve this," said Guardado, mayor of Villa de Ramos, a municipality that includes the men's native village of Zacaton in the northern state of San Luis Potosi.
Guardado identified the men as brothers Jose de Jesus Duenas and Manuel Davila Duenas, 21 and 31; Lino Guardado, 43, and his 21-year-old nephew Conrado Lopez Guardado.
The mayor said he was informed of the deaths the day the bodies were found.
"I prayed to God that it wasn't true, but sadly it is true," he said.
Ohio investigators on Thursday declined to say if they had any leads in the case and have not made public any suspected motive.
But the widespread belief in Villa de Ramos is that the motive was robbery.
"They had just taken out money ... apparently a lot of money," community priest Julian Jimenez told the AP in a separate telephone interview.
"I think it was because they wanted to rob the money they had gotten together," the mayor added, saying the men were killed just days before they were scheduled to return to Mexico to celebrate Christmas with the family.
Hamilton County Coroner O'dell Owens said three of the men apparently were killed in bed. Two showed signs of having struggled with an attacker, and each had been beaten and then stabbed in the heart.
The apartment was sparsely furnished and only one wallet, containing $1,300 in cash, was found there, Owens said. Authorities also found receipts, one for $2,500, indicating the men were sending money to relatives in Mexico.
The Mexican government said Thursday it would pay to repatriate the bodies at a yet-unspecified date. The Mexican government and U.S. immigration authorities also are helping Sharonville police in their investigation. Police have declined to say if they have any leads.
All four men worked as stonemasons, the mayor said. Jose de Jesus Duenas and Lopez had been in the U.S. for four years, while Lino Guardado and Manuel Davila Duenas arrived only eight months ago, he said.
An estimated 11 million Mexicans live in the United States, about 6 million of whom are undocumented.