AJDABIYA, Libya — Col. Muammar el-Qaddafi’s forces retreated from this strategic city on Saturday, running for dozens of miles back along the coast with Libyan rebels in pursuit in their first major victory since American and European airstrikes began a week ago.

The rebels’ advance was the first sign that the allied attacks, directed not only against Colonel Qaddafi’s aircraft and defenses but also against his ground troops, were changing the dynamics of the battle for control of the country. As night fell, rebel forces had recaptured Ajdabiya, a crucial hub city in eastern Libya, and had also driven almost uncontested to the town of Brega, erasing weeks of losses as the airstrikes opened the way.

At the same time, however, Western leaders are debating the ability of the military operation to achieve notably differing goals: to protect Libyan civilians and remove Colonel Qaddafi from power.

President Obama, in his weekly radio address, tried to reassure Americans that the mission was both important and effective. “Today I can report that thanks to our brave men and women in uniform we’ve made important progress,” he said, adding, “We are succeeding in our mission.”