Gadhafi's message was undercut by its delivery - a scroll across the bottom of state TV as he remained out of sight. The White House said the strongman's inner circle was clearly crumbling with the loss of Foreign Minister Moussa Koussa, who flew from Tunisia to England on Wednesday.
Ali Abdessalam Treki, a former foreign minister and U.N. General Assembly president, announced his departure on several opposition websites the next day, saying "It is our nation's right to live in freedom and democracy and enjoy a good life."
Gadhafi accused the leaders of the countries attacking his forces of being "affected by power madness."
"The solution for this problem is that they resign immediately and their peoples find alternatives to them," the Libya state news agency quoted him as saying.
His government's forces have regained momentum on the rapidly moving front line of the battle with opposition forces, retaking the town of Brega after pushing the rebels miles back toward the territory they hold in eastern Libya.
The rebels said they were undaunted, taking heart from the departures in Gadhafi's inner circle.
"We believe that the regime is crumbling from within," opposition spokesman Mustafa Gheriani said in Benghazi, the rebels' de facto capital.
He compared Gadhafi to a wounded animal.
"An injured wolf is much more dangerous than a healthy wolf. But we hope the defections continue and I think he'll find himself with no one around him," Gheriani said.
Most high-level Libyan officials are trying to defect but are under tight security and having difficulty leaving the country, said Ibrahim Dabbashi, the deputy ambassador in Libya's U.N. mission, which now backs the opposition.
Koussa is privy to all the inner workings of the regime, so his departure could open the door for some hard intelligence, though Britain refused to offer him immunity from prosecution.
"Koussa is one of the pillars of Gadhafi's regime since the 1970s," said Abdel Moneim al-Houni, a former Libyan Arab League representative who was among the first wave of Libyan diplomats to defect this month. "His defection means that he knew that the end of Gadhafi is coming and he wanted to jump from the sinking boat."
Libyan officials, who initially denied Koussa's defection, said he had resigned because he was sick with diabetes and high blood pressure. Government spokesman Moussa Ibrahim said Koussa was given permission to go to Tunisia, but the regime was surprised to learn he had flown to London.
"I talked to many people and this is not a happy piece of news, but people are saying, 'So what? If someone wants to step down that's his decision,"' Ibrahim said.
Nations behind the campaign of international airstrikes that have hobbled Libya's military hailed Koussa's resignation as a sign of weakness in Gadhafi's more-than-41-year reign.
White House spokesman Jay Carney said if there was ever a sign that Gadhafi's inner circle was crumbling, Koussa's departure was it.
Koussa "can help provide critical intelligence about Gaddafi's current state of mind and military plans," said Tommy Vietor, U.S. National Security Council spokesman. He added that his defection "demonstrates that the people around Gaddafi understand his regime is in disarray."
In another blow to the regime, U.S. officials revealed Wednesday that the CIA has sent small teams of operatives into rebel-held eastern Libya while the White House debates whether to arm the opposition.
Despite the setbacks and ongoing airstrikes - now led by NATO - Gadhafi loyalists have retaken much of the territory the rebels had captured since airstrikes began March 19.
Rebels had advanced overnight to the west gate of Brega, a town important to Libya's oil industry that has gone back and forth between rebel and loyalist hands. They were in Brega at dawn, but they soon pulled out under heavy shelling from Gadhafi's forces.
Black smoke billowed in the air over Brega as mortars exploded. "There were loads of (rebel) wounded at the front lines this morning," said rebel fighter Fathi Muktar, 41.
Rebels fired back from sand dunes, chanting "Allahu akbar!" or "God is great!" with each rocket fired. Spotters with binoculars watched where they landed and ordered adjustments.
Brega was deserted and Jabbar Ali, 25, a rebel aviation technician, said Gadhafi's forces were at its eastern gates and controlled much of the city.
Many people also have fled Ajdabiya, a rebel-held city about 50 miles (80 kilometers) to the east, for fear that government forces were on their way.
The fighting has highlighted the rebels' weaknesses: Some ran screaming to cars after being frightened by the outgoing fire from their own side.
The U.S. has ruled out using ground troops in Libya but it is considering providing arms to the rebels.
Defense Secretary Robert Gates, however, told Congress on Thursday that the U.S. still knows little about the rebels, and that if anyone arms and trains them it should be some other country.
Asked by a lawmaker whether U.S. involvement might inevitably mean "boots on the ground" in Libya, Gates replied, "Not as long as I am in this job."
NATO is among those saying a new U.N. resolution would be required to arm rebels, though Britain and the U.S. disagree. Several world leaders oppose arming rebels, including Turkish Prime Minister Recep Tayyip Erdogan who said in London that it could "create an environment which could be conducive to terrorism."
Koussa is not the first high-ranking member of the regime to quit - the justice and interior ministers resigned early in the conflict and joined the rebellion based in the east. Koussa, however, is a close confidant of Gadhafi's.
Koussa was Libya's chief of intelligence for more than a decade. The opposition blames him for the assassinations of dissidents in western capitals and for orchestrating the 1988 Lockerbie bombing over Scotland and the bombing of another jet over Niger a year later. The links have never been confirmed.
In later years, however, Koussa played an important role in persuading Western nations to lift sanctions on Libya and remove its name from the list of state sponsors of terrorism. He led settlements of Lockerbie, offered all information about Libya's nuclear program and gave London and Washington information about Islamic militants after the Sept. 11 attacks.
Scottish prosecutors say they've asked Britain's Foreign office to speak with Koussa about the Lockerbie bombing, which killed 270 people.
Meanwhile, U.N. Secretary-General Ban Ki-moon's special envoy, Abdelilah Al-Khatib, arrived Thursday in Tripoli, U.N. spokesman Farhan Haq said. He was also expected to talk to the Libyan opposition, Haq said, without providing details.
Lucas reported from Ajdabiya, Libya. Associated Press writers Ben Hubbard in Benghazi, Edith M. Lederer at the United Nations and Maggie Michael in Cairo contributed to this report.