Many of the leaders who were in Paris had called for Colonel Qaddafi to quit, and it may be that military intervention leads to negotiations with the opposition for the colonel and his family to leave — or, at the least, buys time for the rebels to regroup.

There are risks, though. One widely held concern is the possibility of a divided Libya with no clear authority, opening the door for Islamic extremists to begin operating in a country that had been closed to them. The international effort, called Operation Odyssey Dawn, may also present a double standard: While the West has taken punitive action against Libya, a relatively isolated Arab state, the governments in Bahrain and Yemen have faced few penalties after cracking down on their own protest movements.

The main barrage of missile strikes began around 2 p.m. Eastern time, when the United States Navy fired cruise missiles that struck Libya roughly an hour later, Vice Adm. William Gortney told reporters in Washington. He said the Pentagon had not yet assessed the damage that the missiles had caused and would not be able to do so until dawn broke in Libya.

The missile strikes were the start of what Admiral Gortney called a “multiphase operation” to create a no-fly zone that would allow coalition aircraft to fly over Libya without the risk of being shot down. He would not say whether American aircraft would be involved in enforcing the no-fly zone, but he said that no American aircraft were directly over Libya on Saturday afternoon.

Admiral Gortney cast the United States as the “leading edge” among coalition partners in the opening phase of the attack. But in keeping with Mr. Obama’s and Mrs. Clinton’s emphasis that the administration was not driving the efforts to strike Libya, the admiral and other Pentagon officials repeated that the United States would step back within days and hand over command of the coalition to one of its European allies.