An armada of ships and warplanes from the United States, France, Britain, Canada and other coalition nations came under NATO control after the 28-nation military organisation overcame internal divisions to take over the mission.
US, British, French, Canadian, Danish and Belgian jets have attacked Moamer Kadhafi's ground forces since March 19 under a UN mandate to use "all necessary measures" to protect civilians.
Lieutenant General Charles Bouchard, commander of Operation Unified Protector, said 90 Nato aircraft had flown missions since the alliance took charge at 0600 GMT.
"Those who are acting against the civilian population and civilian centres, you would be ill-advised to continue such activities, I recommend that you cease these activities," Bouchard told reporters via videolink from his headquarters in Naples, Italy.
Admiral Giampaolo Di Paola, head of Nato's military committee, said the mission would end once Kadhafi has complied with the UN Security Council resolution, which demands a ceasefire and an end to attacks on civilians.
"When the people will not be threatened or attacked, that will be when we have accomplished our task," Di Paola said, adding that a political solution was needed to resolve the conflict, not just military means.
The admiral denied that Nato was coordinating its operations with the rebels.
Asked about reports that the CIA was on the ground in Libya, Di Paola said Nato does not question the source of intelligence it receives from allies.
The alliance stressed it would stick to the UN mandate to shield civilians, as Di Paola said Nato has not discussed deploying troops while Nato chief Anders Fogh Rasmussen reiterated his opposition to arming the rebels.
Di Paola said some 20 Nato allies are providing assets for one or all three operations under alliance control -- the strikes on ground forces threatening civilians, a no-fly zone, and an arms embargo.
But key Nato members have voiced unease about the bombing missions.
Bouchard vowed that Nato pilots would conduct their missions "with care and precision" in order to "avoid harming the people of Libya."
The general launched a probe into allegations made by a Tripoli-based Italian bishop who said dozens of civilians were killed during coalition bombings. No date was given for the incident, which could not be independently verified.
Turkey, Nato's sole Muslim member, criticised the scope of the coalition strikes that began on March 19 and has made clear its planes would not take part in any air strikes.
Another major Nato member, Germany, refused to vote for the UN Security Council resolution that authorised the use of force and will stay out of the offensive operations.
The Netherlands has contributed planes but they will only participate in a no-fly zone to prevent hostile jets from flying, not the strikes against other targets.
NATO wants to bring outside partners into the mission, especially Arab nations. Qatar and the United Arab Emirates are the only Middle Eastern nations to have provided jets.
Sweden, a Nato partner but not member, offered fighter jets but said it would not conduct ground strikes.
The United States, already stretched after a decade of combat in Afghanistan and a fragile situation in Iraq, had been eager to hand over control of the mission to someone else.
Attempting to convince a war-weary public about his decision to intervene in Libya, US President Barack Obama vowed Wednesday that the US military would reduce its own involvement, playing only a supporting role.