By Devon M. Sayers, CNN

(CNN) — Attorneys representing detainees held at the controversial makeshift immigration detention center dubbed “Alligator Alcatraz” are in federal court Monday seeking to allow detainees to meet with attorneys.

The attorneys from groups including the ACLU, the US Immigration Law Counsel and Florida Keys Immigration filed a lawsuit against Department of Homeland Security Secretary Kristi Noem, Florida Gov. Ron DeSantis and other officials in July, saying the defendants “blocked detainees held at the facility from access to legal counsel” and are preventing “people detained in civil immigration custody at Alligator Alcatraz from communicating with legal counsel and from filing motions with the immigration court that could result in their release from detention.”

The lawsuit also aims to ensure there is updated information about the location of the detainees at “Alligator Alcatraz.”

“The U.S. Constitution does not allow the government to simply lock people away without any ability to communicate with counsel or to petition the court for release from custody. The government may not trample on these most fundamental protections for people held in its custody,” Eunice Cho, senior counsel with the ACLU’s National Prison Project and the lead attorney in the case, said in a news release.

The Department of Homeland Security has denied the allegations, telling CNN in a statement Sunday the “facility maintains a physical space for attorneys to meet with their clients,” and that attorneys may also request to speak with detainees they represent via email.

At a hearing last month, attorneys for the ACLU urged the judge to move forward with the lawsuit as quickly as possible, alleging that staff at the detention center were pushing the detainees to self-deport without access to counsel. The ACLU also reminded the court that “removal flights” from the facility had already taken place.

“The government has banned in-person legal visitation, any confidential phone or video communication, and confidential exchange of written documents,” the ACLU said in the news release about the lawsuit, describing several instances of attorneys turned away after attempting to meet with their clients.

Monday’s hearing in Miami, Florida, is the latest in the case against the federal and state officials whose attorneys have argued the lawsuits were not filed in the correct federal court district.

US District Judge Rodolfo Ruiz II, who was nominated by President Donald Trump, appeared skeptical of those arguments. The judge also said there was “confusion” about who runs the detention camp.

“Alligator Alcatraz” is purportedly run by the state of Florida under a partnership with local agencies and the United States Immigration and Customs Enforcement under a federal program known as the 287(g) program.

Deep in the marshy wetlands of the Florida Everglades, “Alligator Alcatraz” has been mired with controversy since the start, with reports of hundreds of migrants confined in cages amid sweltering heat, bug infestations and meager meals.

“What is happening at the facility is anomalous for many reasons, not only the way that it was built and where it’s been built, the legal authority and the confusion about who is running the detention facility and whose custody people are in,” Cho told CNN. “These are all things that have never really been seen at other detention facilities.”

The state of Florida has pushed back, saying conditions at the camp are in “good working order” and that claims to the contrary are false.

Cho explained the goal of their case is make sure “basic constitutional rights” of detainees are being upheld, including the “basic right to be able to speak to their lawyers and the basic right to be able to petition the government for release from custody.”

Other alleged violations of constitutional rights include officers “pressuring detainees to sign voluntary removal orders without the opportunity to speak to counsel,” said Cho, and a detainee who was deported after their bond hearing was canceled because immigration courts said they don’t have jurisdiction over people who are held in “Alligator Alcatraz.”

“These are fundamental constitutional rights, and the fact that it’s been happening for such a long time has had a huge impact on the people who are being held at this facility,” Cho said.

“Alligator Alcatraz cannot end up being a black hole where people disappear.”

The hastily built detention center is about an hour’s drive west of Miami. The temporary camp is built on an airstrip and made up of repurposed FEMA trailers and tents, surrounded by a fence.

This lawsuit against the facility is one of two working its way through the federal court system – the other was filed by environmentalists suing to stop the facility’s operations due to its close location to the marshlands that serve as a crucial source of freshwater and drinking water for South Florida.

On Thursday, DeSantis announced a new immigrant detention center called “Deportation Depot” in northern Florida. The facility will likely be ready in about two to three weeks, Florida Division of Emergency Management Director Kevin Guthrie said, and it is expected to house around 1,300 detainees.

CNN’s Rafael Romo and Maxime Tamsett contributed to this report.

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