Graham said using lethal force against Gadahn, a spokesman for the terrorist network, "is appropriate and should be utilized without hesitation," Roll Call reported Monday.
"Adam Gadahn is an American citizen who has aligned himself with al-Qaida," Graham said in a statement. "He should be considered an enemy combatant not a common criminal. And even though he is an American citizen, he should be subject to being killed or captured by our military and intelligence forces."
If Gadahn is captured, he should not be read his Miranda rights "but held as an enemy combatant under the Law of War for intelligence gathering purposes," Graham said.
"As a senior al-Qaida operative his deeds and actions put our nation at risk," Graham said.
The South Carolina Republican also posted on his Twitter page comments about his views on Gadahn.
Roll Call said Graham has long held that reading Miranda rights to terrorists is "counter-productive." More recently he called for the Boston Marathon bombing suspect, a naturalized citizen, to be detained without being Mirandized.