Two civil rights groups are suing the US to try to get a licence to represent the father of Muslim cleric Anwar al-Awlaki in a case against the CIA.
Nasser al-Awlaki contacted the American Civil Liberties Union (ACLU) in July when his US-born son appeared on a CIA "capture or kill" list.
The US then labelled Anwar al-Awlaki a "specially designated global terrorist" - making it illegal to serve as lawyers for his benefit without a licence.
That has delayed his father's case.
The ACLU and the Center for Constitutional Rights filed a lawsuit to obtain the licence to challenge the CIA over its "capture or kill" order at a US district court in Washington DC.
The ACLU was contacted by Nasser al-Awlaki because of the US government's decision to authorise the targeted killing of his son.
The cleric, who is thought to be a senior operative for al-Qaeda in Yemen, has been linked to a deadly shooting at Fort Hood army base in Texas and an attempted bombing of a US airliner on 25 December.
The ACLU's deputy legal director Jameel Jaffer said the group's lawsuit did not aim to have Mr Awlaki's name removed from the CIA's "capture or kill" list - but rather to have the CIA "articulate the legal standard under which the government can target Americans for killing without trial, charge, or conviction".
"The challenge we anticipate bringing [to the CIA] relates to the standard under which the government decides whether it can kill a US citizen without charge or trial," Mr Jaffer said.
The case would have been the first challenge to the CIA's target list, the ACLU said.
But soon after Mr Jaffer and another lawyer flew to Yemen to speak to Naseer al-Awlaki about the case, the US Treasury Department's Office of Foreign Assets Control (OFAC) put his son on a second list.
The cleric's addition to the "specially designated global terrorist" list made it illegal for lawyers to represent him or his interests without authorisation.
"The government is targeting an American citizen for death without any legal process whatsoever, while at the same time impeding lawyers from challenging that death sentence and the government's sweeping claim of authority to issue it," ACLU executive director Anthony Romero said in a statement.
The rights group said the US Treasury Department had not responded to its request for permission to represent his father in the case.
A Treasury Department spokesperson said there were more than 4,000 individuals and entities on the "specially designated global terrorist" list, and the recent decision to include Mr al-Awlaki was unrelated to the ACLU's pending lawsuit against the CIA.
Meanwhile, US news network CNN reported on Tuesday that Anwar al-Awlaki might be next in line to fill Osama Bin Laden's shoes as leader of al-Qaeda.
The cleric has posted sermons on the internet thought to have inspired new recruits to Islamist militancy.