Calling the suit "unprecedented and extraordinary," Douglas Letter, a lawyer for the administration, argued that if the government were to lose the case it would give courts the ability to "look over the shoulder" of the president as he make decisions regarding national security threats.
Two public interest groups, the American Civil Liberties Union and the Center for Constitutional Rights, have filed the suit on behalf of Anwar al-Awlaki's father, Nasser al-Awlaki.
They are seeking a declaration from the court that the Constitution and international law prohibit the government from carrying out targeted killings outside of armed conflict, except as a last resort to protect against imminent threats of death.
In court, Jameel Jaffer of the ACLU argued that -- short of a court-ordered injunction -- the president will have the "unreviewable authority to order the assassination of any U.S. citizen." Letter called such a claim "absurd" and reiterated that Awlaki has been formally designated as a global terrorist who has attempted to carry out operations to kill Americans.
ABC News' Martha Raddatz has reported President Obama himself has authorized the targeted killing of Awlaki in Yemen, where he is believed to be hiding.
Awlaki is a member of al Qaeda in the Arabian Peninsula and has been linked to the attempted bombing of Northwest Airlines Flight 253 on Christmas day 2009, the shootings at Fort Hood in Texas by Army Maj Nidal Hasan, and the recent seizure of bomb making materials in the cargo of two planes.
In court the government refused on several occasions to address the issue of whether Awlaki is on a government kill list, but argued that the elder Awlaki is essentially asking the judiciary to step into an area at the core of the power of the President and in essence seeking an "injunction against the president."
Letter said it is "fundamentally inconsistent with Constitutional construction."
The government contends that the case should be dismissed because the father has no legal right to bring the suit when the younger Awlaki could do so on his own behalf. The government contends that Awlaki "holds the key to his own safety."
"Why shouldn't I conclude -- in light of public comments made by Anwar al Awlaki ... that he has no desire to bring this case?" U.S. District Court Judge John Bates asked Jaffer, referring to videos released by Awlaki asking that Americans be killed without reason.
On another he said, "Why can't Anwar al Awlaki simply emerge from hiding and have full access to the courts?"
Letter asserted that if Awlaki surrendered the whole case would go away: "He is under no threat from lethal force."
But Jaffer said that Awlaki was unable to assert his rights because he is under a death threat. "They are imposing the death penalty without trial."