Moammar Gaddafi’s wife and three of his children have apparently fled across the border into Algeria, underscoring how much of Libya has slipped out of the control of the former autocrat, who ruled the country for about 42 years.

But there was still no indication where Gaddafi was hiding. Rebel leaders fear that violence will continue until Gaddafi is captured and Libyans can see that he is no longer in power. A businessmen’s club in the eastern rebel stronghold of Benghazi has offered a $2 million bounty for him.

The Algerian foreign minister said in a statement that Gaddafi’s wife, Safia, his daughter Aisha and two of his sons, Mohammed and Hannibal, crossed into Algeria by land.

The statement, reported by the Algerian state news agency, also said that Algerian authorities alerted the U.N. secretary general, the president of the U.N. Security Council and the head of the Libyan rebels’ Transitional National Council, Mustafa Abdel Jalil.

The U.S. State Department said it had not independently confirmed the report, and it was unclear Monday night whether Abdel Jalil had been contacted. He was en route to Libya from Qatar.

The rebel council demanded the immediate extradition of the Gaddafi family members to Libya. Abdel Jalil has said that all top Gaddafi loyalists will face “fair” trials in Libya.

“Some of his children are accused of committing crimes in Libya,” said Ahmed Jibril, a spokesman for the council’s foreign affairs ministry and a former Libyan diplomat. “We hope Algeria cooperates.”

Gaddafi’s children have played important roles in their father’s regime. Mohammed was the head of the Olympic committee and chairman of the General Posts and Telecommunications Co., which cut off phone and satellite services to the east when the uprising began. Hannibal was the head of the General National Maritime Transport Co. Some of Gaddafi’s sons, including Khamis, led military brigades that actively suppressed the revolt.

Rebel leaders also said this week that they believe Khamis was killed in fighting southeast of Tripoli, the capital.

They said they weren’t surprised to hear that Gaddafi’s family members had fled to neighboring Algeria. The Libyan opposition has long accused Algeria of aiding Gaddafi’s forces and supplying mercenaries to violently put down the revolt. Algeria has yet to recognize the council as the only legitimate governing body in Libya.

“Algeria is the only solution” for Gaddafi’s family, said Mustafa el-Sagazly, the deputy interior minister of the rebel council. “The council will demand their return, but it’s in the hands of Algeria. It will take a long time and negotiations.”

Jibril added that council officials are concerned that Gaddafi and his other children, including Saif al-Islam, may also have crossed into Algeria. Gaddafi and Saif al-Islam are wanted by the International Criminal Court in The Hague.

“We want to see justice and accountability for Gaddafi and those members of his family with bloods on their hands and those members of his regime with blood on their hands,” State Department spokeswoman Victoria Nuland said. “But it will be a decision of the Libyan people how that goes forward.”"

In another development, Libyan opposition leaders have ruled out any major role for foreign peacekeepers in the country, insisting that a new transitional government will take the lead in establishing security, according to top U.N. officials.

The decision, which has been detailed in high-level talks involving representatives of the Transitional National Council, U.N. officials and foreign governments over the past week, reflects the opposition’s growing confidence in its ability to manage any security vacuum in the country. Abdel Jalil said last week that the council might consider asking police forces from other Muslim countries to help secure Libya.

Although Gaddafi’s regime has apparently crumbled, rebel fighters are still grappling with pockets of resistance. Regime loyalists still control Gaddafi’s home town, Sirte, which is between Benghazi and Tripoli. Rebel leaders are trying to negotiate a truce, but they plan to use military force if negotiations fail.

Staff writers Joby Warrick in Washington and Colum Lynch at the United Nations contributed to this report.