The group represents a large share of the detainees remaining who are not facing trial in a military court process at the prison, which President Trump has promised he will keep open and potentially use to house new terrorism suspects.
Wells Dixon, a senior staff lawyer at the Center for Constitutional Rights, which was involved in putting forward this week's action, said the Trump administration had opened itself up to a legal challenge because it appeared to intend to leave inmates at Guantanamo for the foreseeable future, even those who face no charges.
The motion argues "really for the first time, that the men who remain at Guantanamo simply have been held for too long," Dixon said. "These men will likely die in Guantanamo unless the courts intervene."
A spokeswoman for the Justice Department declined to comment, saying that officials were reviewing the filing.
The new legal action could present a test of the Trump administration's resolve in keeping the controversial prison in operation and breaking with the previous administration's practice of releasing detainees overseas, which many Republicans allege has threatened American security.
With 41 prisoners remaining, the population at Guantanamo is a fraction of the more than 700 it housed in the wake of the 2001 attacks on New York and Washington.
Trump, criticizing the actions of his predecessor, vowed after his election that he would end detainee transfers and fill the detention facility, perched on a corner of Cuba, with "bad dudes."
Trump has backed off that promise in recent months, suggesting that it would take too long to try the suspect in a November terrorist attack through the dysfunctional process for trying Guantanamo detainees. More than 16 years after the 9/11 attacks, trials for those suspects are stuck in years of logistical and security delays and could be years away from conclusion.
A spokesman for the National Security Council, speaking on the condition of anonymity because he was not authorized to comment, said decisions regarding "terrorists" were made on an individual basis, grounded in the particulars of each case. "President Trump remains committed to using military detention and all available tools to defeat terrorism and protect the United States and its interests abroad," he said.
Several of the men included in Thursday's filing were granted approval to be resettled overseas after undergoing a security review by the Obama administration but did not end up being among the 196 inmates repatriated or sent to a third country.
The highest-profile prisoner in the group is Abu Zubaida, an alleged al-Qaeda operative who was tortured at a secret CIA facility before being brought to Guantanamo in 2006.
In their filing, the attorneys for the detainees argue that the Trump administration's decision not to consider resettlement or alternative arrangements for detainees who have not been charged violates their due-process rights.
A spokeswoman for the Pentagon said the Periodic Review Board process, which convenes officials from across the government to consider whether a detainee continues to pose a risk, has continued.
But the Trump administration has not appeared to use that review mechanism to move prisoners toward overseas transfer.
Lee Wolosky, who served as special envoy for Guantanamo closure under the Obama administration, said the Trump administration's approach "flies in the face of the history of U.S. detention policy under both Republican and Democratic administrations."
The motion also argues that the ongoing detention of two men already cleared for transfer, a Yemeni and a Moroccan, has no legal purpose, because the Trump administration does not intend to move them overseas.
Also at issue is the Authorization for Use of Military Force, passed in the wake of the 9/11 attacks. It has been cited as a basis for military detentions and ongoing combat operations overseas, but attorneys for the 11 men assert it does not justify indefinite imprisonment.
Jack Goldsmith, a professor at Harvard Law School who has written extensively about national security issues, said that assertion, and the argument that the Trump administration has failed in its responsibility to examine each detainee's case individually, is unlikely to succeed in court.
"It is doubtful but conceivable that those arguments could get traction," Goldsmith said in an email, also referring to the motion's argument that Trump has already lost legal challenges that assert he has demonstrated bias against Muslims.
Matt Zapotosky contributed to this report.