U.S. officials said Abu Khattala was captured Sunday and is currently in U.S. custody “in a secure location outside Libya.”
McCain told reporters the capture is "good news" and added that he's "very glad to hear it." He indicated that he knew the operation was in the works but noted that the suspect had been giving interviews to TV reporters in recent years.
"Obviously he should be put on trial. I'd bring him to Guantanamo. Where else can you take him to?" McCain asked.
Graham insisted that the suspect must be treated as an enemy combatant and not read Miranda rights.
"I hope we gather intelligence through the law of war interrogation," Graham said. "He should be going to Gitmo."
While emphasizing that he does not endorse torturing the suspect, Graham said he wants the him interrogated in a military holding facility such as Guantanamo Bay for an extended period of time.
"It would be the biggest mistake for the ages to read this guy his Miranda rights," Graham said. "We should have some quality time with this guy, weeks and months. Don't torture him - but have some quality time."
On Twitter, Graham said that holding Abu Khattala on a ship amounts to a "haphazard" approach.
Rubio said in a statement that the suspect should immediately be transferred to Guantanamo "for detention and interrogation." Cruz said he "belongs in Guantanamo and in the military justice system, not in the U.S. civilian court system with the constitutional protections afforded U.S. citizens."
Some Democrats, including Sen. Dick Durbin (D-Ill.), pushed back against the suggestion that the suspect must be held at Guantanamo.
"What a surprise!" Durbin declared, throwing his hands up in the air, when told by reporters about comments from McCain and Graham.
Durbin and others noted that several hundred terror suspects have been tried and convicted in federal courts while military courts - which is where the suspect would be tried if he were sent to Guantanamo - produced much longer legal proceedings that have so far led to only several convictions.
"If you're keeping score on this ... I think I can count on one hand all those who have been prosecuted by military commissions," Durbin said. "It's a tired response by their side."
That sentiment was echoed by Sen. Patrick Leahy (D-Vt.), who called for Guantanamo Bay to be closed.
"Oh for God's sake," he declared when told by reporters about what McCain and Graham said.
"With all of these terrorists we've had four or five convictions in military courts, we've had several hundred convictions in federal courts." Leahy said. "Do the math."
Told of the criticism from Democrats, McCain doubled down on his calls for the suspect to be held at Guantanamo, saying anything else would be "totally inappropriate."
Asked about the line of argument that more convictions of terrorists are won in military courts, McCain replied "I've heard that argument but I don't agree with it."
Sen. Kelly Ayotte (R-N.H.) said she is "pleased that Khattala is finally in U.S. custody," and "grateful for the military, intelligence, and law enforcement professionals who helped capture him."
But Ayotte also offered a note of caution, saying, “Rather than rushing to read him his Miranda rights and telling him he has the right to remain silent, I hope the administration will focus on collecting the intelligence necessary to prevent future attacks and to find other terrorists responsible for the Benghazi attacks.”
Sen. Saxby Chambliss (R-Ga.), the ranking Republican on the Senate Intelligence Committee, told reporters, "It's good news. This is a guy we've been after and we've had our eyes on him. It was a very good operation that was carried out, obviously successful operation. He's being interrogated right now and we hope we find out some positive things. But I'm really encouraged by finally getting some good news on Benghazi.'
Chambliss added, "They've been in touch with us for the last several days on this." He said he knows where the suspect is being held and that more on that would come later.
House Armed Services Committee Chairman Howard "Buck" McKeon (R-Calif.) said in a statement that Abu Khatalla should "be fully interrogated" before "before any prosecution process begins."
House Speaker John Boehner (R-Ohio) thanked the military and FBI in a statement and called the capture "good news." He added, "I look forward to hearing more details regarding the raid, and I expect the administration to give our military professionals time to properly gather any useful intelligence he has.”
Senate Intelligence Committee Chairman Dianne Feinstein (D-Calif.) had no comment.
President Obama said in a statement that, "With this operation, the United States has once again demonstrated that we will do whatever it takes to see that justice is done when people harm Americans. We will continue our efforts to bring to justice those who were responsible for the Benghazi attacks."
On Twitter, former top Obama adviser David Plouffe praised both the president and the personnel who made the capture:
Once again our Special Forces execute flawlessly. And once again a President keeps his commitment.
— David Plouffe (@davidplouffe) June 17, 2014
Updated at 1:59 p.m.