"You have to reserve to your commander in chief the authority to act in emergencies," said Thune, according to the Rapid City Journal.
Thune, who had been considered a possible Republican candidate for president, announced last month that he would not seek the White House in 2012.
Thune said that, if the fight becomes protracted, Obama must to go to Congress for permission to continue.
"I do think if there is any kind of sustained operation there, then Congress needs to be involved," Thune said.
In the past week a wide range of voices from Congress including Sen. Rand PaulRand PaulConquering Trump returns to conservative summit Rand Paul rejects label of 'Trump's most loyal stooge' GOP healthcare plans push health savings account expansion MORE (R-Ky.), Rep. Dennis Kucinich (D-Ohio), Rep. Anthony Weiner (D-N.Y.) and Rep. Tom McClintock (R-Calif.), have argued that Obama erred in initiating the attack without receiving congressional approval.
Other lawmakers have supported the president’s actions.
Thune’s approval did not come without reservations.
"I think we have to ask the question, 'What is the vital American national security interest?'" Thune said. “What's the end game here? How do we define this mission? There's been a lot of confusion and a lot of ambiguity about that, and that's not good."