“He is supposed to be out of Libya for a couple of days,” Mr. Ibrahim said.

But Mr. Ibrahim added that the government’s struggle against a rebel uprising “doesn’t depend on individuals, even if they are high-ranking officials,” and that, in any case, whether Mr. Ghanem defected was “his business” — statements that appeared to suggest that the Qaddafi government knew that Mr. Ghanem had defected. If so, it would not be the first high-level defection among Colonel Qaddafi’s associates.

Moussa Koussa, who was the foreign minister, defected in March and spent time in London being questioned by British intelligence officials before leaving for Qatar. A former justice minister in Tripoli, Moustafa Abdul Jalil, heads the rebels’ national transitional council. A former interior minister, Abdul Fatah Younes, who had been one of the top generals in the Qaddafi forces, has also joined the rebels, serving as their military chief of staff.

The defections have added to the deepening isolation around the Qaddafi government since the uprising began three months ago. On Monday the chief prosecutor of the International Criminal Court in the Hague sought arrest warrants for Colonel Qaddafi, his son Seif al-Islam el-Qaddafi and the colonel’s brother-in-law on charges of orchestrating systematic attacks against civilians. Qaddafi loyalists fighting a rebel army in the contested city of Misurata, 130 miles east of Tripoli, retreated last week, losing control of the city’s airport.