The Center for Constitutional Rights and the American Civil Liberties Union said they agreed to pursue the case in July at the request of the father of Anwar Al-Awlaki, a cleric born in New Mexico.
US authorities have tied Nasser Al-Awlaki's son to the failed bombing attempt of a US commercial jet on Christmas Day in 2009 and also to an Army major who went on a shooting spree that killed 13 people last year at Fort Hood in Texas.
The US Treasury Department last month blacklisted Anwar Al-Awlaki as a "specially designated global terrorist," saying he is a leader of Al-Qaeda hiding in Yemen. The administration in April authorized operations to capture or kill him.
The ACLU and CCR said that as a result of the Treasury's designation, they can no longer provide legal services to the father without permission because it would benefit his son. Despite requesting authorization, the Treasury Department has not responded, they said.
The two groups sued in US District Court for the District of Columbia challenging the restriction on legal services. If they win, they plan to file suit on behalf of Al-Awlaki's father challenging the order to capture or kill the cleric.
"We don't believe we should have to play 'mother may I' with the government when we want to challenge the government's efforts to kill an American citizen outside the theater of war and without due process," said ACLU Executive Director Anthony Romero.
The Treasury Department had no immediate comment.
In its lawsuit, the groups asked for the court to block the restriction on legal services or order the Treasury Department to issue permission so they can pursue a challenge against the authorization to capture or kill him.
Without the Treasury Department's authorization, the two groups said they could face legal repercussions and prosecution if they represented the father, even if they do so for free.
While US authorities have tied Al-Awlaki to the Christmas bombing attempt and the Fort Hood shooting spree, no charges have been publicly filed against him.
White House spokesman Robert Gibbs deflected questions about what legal process was used to issue the order against the cleric. "There's a process in place that I'm not at liberty to discuss," he said.
"Let's not take a tourist who might visit Italy overseas and equate him with somebody who has on countless times in video pledged to uphold and support the violent and murderous theories of Al-Qaeda," Gibbs said.
A US Treasury official said last month that Al-Awlaki is the fourth person with a US passport or Social Security number to receive such a terrorist designation since the executive order was put in place during the George W. Bush administration in 2001, shortly after the Sept. 11 attacks.
