BY THE TIME President Obama addressed the country about Libya Monday evening, the mission was nine days old — and he could point to some clear successes. The United States, he said, “has worked with our international partners to mobilize a broad coalition, secure an international mandate to protect civilians, stop an advancing army, prevent a massacre and establish a no-fly zone.” In fact, there’s little doubt that the first allied airstrikes stopped an assault on the rebel-held city of Benghazi by the forces of Moammar Gaddafi that could have killed thousands. Mr. Obama was right to act, and he deserves the credit that he claimed.

The problem is that the war in Libya is far from over, even if the administration is handing command off to the NATO alliance. Mr. Obama said “the United States will play a supporting role” from now on, and “the risk and cost of the operation . . . will be reduced significantly.” But he also recognized that unless Mr. Gaddafi is removed from power, “Libya will remain dangerous.” The humanitarian rescue that the president celebrated will be tenuous — and American forces may be needed again.

For now, a change of regime does not look near. While rebel forces have made encouraging advances in recent days, it’s not clear they are capable of a military victory without direct support from NATO. Such backup is not allowed by the U.N. resolution that authorized the intervention, and Mr. Obama reiterated that he would not support it: “Broadening our military mission to include regime change,” he said, “would be a mistake.”

Mr. Obama said he would “actively pursue” Mr. Gaddafi’s downfall “through non-military means.” But his elaboration of that strategy was less than satisfying. While pointing to the financial sanctions and arms embargo applied to the regime by the United Nations, he didn’t endorse other measures, favored by France, that might speed an opposition victory: supplies of weapons or training for the rebel army, for example.

The president repeated calls for those around Mr. Gaddafi to turn against him. The administration appears to hope that the regime will crumble from within. “With the time and space that we have provided for the Libyan people, they will be able to determine their own destiny,” Mr. Obama declared. But how?

What was missing from Mr. Obama’s address was a strategy that doesn’t rely on good fortune — a sudden coup, an unexpected rebel advance, or an unlikely political deal for Mr. Gaddafi’s departure. The president is not wrong to try to limit the costs and risks of intervention in Libya when U.S. forces are still deployed in two other Muslim countries and a fiscal crisis presses at home. But a policy that curtails American involvement at the expense of failing to resolve Libya’s crisis may only lead to greater costs and dangers.

Mr. Obama concluded by broadly endorsing the uprisings across the Middle East and declaring that “this movement of change cannot be turned back” and that “we must stand alongside those who believe in the same core principles” of freedom and nonviolence. He is right to stake out that position, and to argue that the United States “can make a difference.” U.S. intervention has helped make a difference in Libya; the danger is that the president’s eagerness to circumscribe American involvement will ultimately thwart the change he endorsed.