Republican and Democratic members of Congress appearing on Sunday morning news shows praised the U.S. operation in which Islamic State operative Abu Sayyaf was killed.

However, Republicans generally qualified their praise by pointing to larger concerns about national security.

"Well, for now let's just say it was a successful raid," Sen. Marco Rubio (R-Fla.) said on "Fox News Sunday." "And it's good news. Obviously, anytime you can degrade or take away top leadership of an organization, it's a positive step forward."

But, Rubio, a presidential candidate, added: "It doesn't take away from the fact that ISIS remains a group that just in the last 48 hours has captured yet another critical city within Iraq and continues to be a dangerous group." ISIS is an alternative acronym for the Islamic State, which launched an attack on Ramadi late last week and has since captured the city.

Abu Sayyaf, a Tunisian who was killed early Saturday in an attempt to capture him, was described by a U.S. defense official as “fairly high up” in the Islamic State hierarchy.

"Well, the president has done a good job with these special operations type missions," Senate Majority Leader Mitch McConnell (R-Ky.) said on ABC's "This Week with George Stephanopoulos." "Where I think the administration has fallen down is they tend not to favor, generally speaking, capture and interrogation. Although it’s good that the wife of this terrorist was captured and will be interrogated. I’ve been distressed, for example, about the willingness to release prisoners at Guantanamo."

Sen. Dianne Feinstein (Calif.), the top Democrat on the Senate Intelligence Committee, lauded the operation.

"Well, my assessment is that it was a success, that it is the kind of one-two punch that we should do more of," she said on "This Week." "I believe that if we're not going to put troops on the ground, then we've got to use our Special Operations forces to go in and collect intelligence; also be able to capture people that might be able to be helpful."

Rep. Adam Schiff (Calif.), the top Democrat on the House Intelligence Committee, called Abu Sayyaf "the guy we were trying to get" and commended the American troops involved. But he added a word of caution.

"Our intelligence was good, but, nonetheless, this was an extraordinary risk. if one of our people were captured, if we lost some of our Special Forces, there would be tough questions to answer about whether it was worth it, and notwithstanding the success of the operation, we will still have to ask the questions," Schiff said on CNN's "State of The Union."