Immigration and Customs Enforcement (ICE) said 11 detainees at the El Paso Processing Center have been refusing food, some for more than 30 days.
Detainees who spoke to the Associated Press, along with a relative and a lawyer representing hunger strikers, said nearly 30 detainees from India and Cuba have been refusing to eat and some are now so weak they cannot stand up or talk.
Another four detainees are on hunger strikes in the agency's Miami, Phoenix, San Diego and San Francisco areas of responsibility, said ICE spokeswoman Leticia Zamarripa on Wednesday.
The men say they stopped eating to protest verbal abuse and threats of deportation from the guards. They are also upset about lengthy lockups while awaiting legal proceedings.
In mid-January, two weeks after the immigrants stopped eating, a federal judge authorised force-feeding of some El Paso detainees, Zamarripa said.
She did not immediately address the detainees' allegations of abuse but did say the El Paso Processing Center would follow the federal standards for care.
ICE officials say they closely monitor the food and water intake of detainees identified as being on a hunger strike to protect their health and safety.
US President Donald Trump's administration has implemented a crackdown on immigration, sending thousands of troops to the US-Mexico border, allowing the government to shut down for 35 days over his demand for a border wall and promising to cut the number of refugees entering the country to a historic low.
The men with nasal tubes are having persistent nosebleeds and are vomiting several times a day, Amrit Singh told the Associated Press. Singh's two nephews from the Indian state of Punjab have been on hunger strike for about a month.
"They are not well. Their bodies are really weak, they can't talk and they have been hospitalised, back and forth," said Singh, from California.
"They want to know why they are still in the jail and want to get their rights and wake up the government immigration system."