Updated: 11:18 a.m.

Sen. Lindsey Graham on Sunday applauded a NATO missile strike in Libya that reportedly killed a son of leader Moammar Gadhafi and three of his grandchildren.

“I think this is a good move by NATO to go after the source of the problem,” the South Carolina Republican said on “Fox News Sunday.” “If you want to protect the Libyan people, go after his inner circle. … In my opinion, wherever Gadhafi goes is a legitimate military target. He’s the command and control source. He’s not the legitimate leader of Libya, and the way to get this to end is to go after the people around him and his support network. So I support what NATO’s doing.”

Graham, who is a member of the Senate Armed Services Committee, said he favors a “pour it on approach” to end the military intervention in Libya, which began last month after the United Nations Security Council adopted a resolution calling for military action to protect Libyan civilians from Gadhafi’s crackdown on political dissidents.

The United States initially sent aircraft into Libya as part of an international coalition to support the Security Council resolution, but it has since pulled back into a supporting role. Graham said he supports sending U.S. aircraft back into the North African nation, and he has repeatedly criticized the administration for being too slow to respond to Gadhafi’s crackdown on the nation.

“In my view, he’s not a foreign leader. In my view, he’s a murderer,” Graham said of Gadhafi. “He’s killing his own people, he’s acting outside of international law, he’s bombing civilians, he’s not the legitimate leader of Libya. … He should be brought to justice or killed.”

Sen. Kent Conrad, who is a member of the Intelligence Committee, was more cautious about whether Gadhafi can be legally targeted as an individual.

“We have legal issues I’m not an expert on,” the North Dakota Democrat said on “Fox News Sunday.” “It is stated policy that we are not targeting an individual, but we can target the pillars of his power.”

He listed the pillars as regiments controlled by Gadhafi’s sons, foreign mercenaries, money and his tribe.

“I believe all of those should be targeted and aggressively gone after. You cannot allow him to continue,” Conrad said.

Senate Armed Services ranking member John McCain warned Sunday that it’s not a simple matter to assassinate Gadhafi.

“It’s not as easy as you think,” the Arizona Republican said on CBS’ “Face the Nation,” pointing out that the United States is still hunting al-Qaida leader Osama bin Laden. “And so, we should be taking out his command and control, and if he is killed or injured because of that, that’s fine. But we ought to have a strategy to help the rebels succeed and overthrow Gadhafi and everybody associated with him.”

McCain said that he is dissatisfied with the United States’ “back seat” role in the military operation in Libya and that NATO allies don’t have ample resources for the fight. He wants the United States to send its air assets into Libya, but he remains opposed to sending ground troops, he added.

The United States has to “understand that right now, unless somehow Gadhafi falls from within, that we may have a stalemated situation, and that would be very bad,” McCain said. “It’s events on the ground that will drive Gadhafi’s desire to leave or not to leave. Right now, in many respects, he’s not doing too badly for a third-rate military power.”

Libyan government spokesman Moussa Ibrahim said Gadhafi and his wife were inside the house targeted by NATO, but they escaped. However, Gadhafi’s son, Seif al-Arab Gadhafi, 29, and three grandchildren under the age of 12 were killed, he added, according to the Washington Post.

NATO acknowledged that it struck a “command and control building” in Tripoli late Saturday but did not confirm the deaths of Gadhafi’s relatives.

“All NATO’s targets are military in nature and have been clearly linked to the Qadhafi regime’s systematic attacks on the Libyan population and populated areas. We do not target individuals,” Lt. Gen. Charles Bouchard, commander of the NATO operation, said in a statement.

“I am aware of unconfirmed media reports that some of Qadhafi’s family members may have been killed,” he added. “We regret all loss of life, especially the innocent civilians being harmed as a result of the ongoing conflict. NATO is fulfilling its UN mandate to stop and prevent attacks against civilians with precision and care — unlike Qadhafi’s forces, which are causing so much suffering.”