It is not the first time Colonel Qaddafi has survived such a close call. In 1986, the United States struck his compound in retaliation for a terrorist attack on a German nightclub frequented by American service members. Colonel Qaddafi has incorporated his survival into his cult of personality, preserving the wreckage of the building as a “Museum of Resistance” and erecting a statue of a giant fist grabbing an American warplane.

Although several of Colonel Qaddafi’s seven sons and one daughter play major roles in the Libyan economy and government (including an older brother with a similar name, Seif al-Islam el-Qaddafi), the son reported killed had been considered a black sheep, believed to spend much of his time in Munich. Many Libyans said they had never seen his picture. In 2007, the German newspaper Der Spiegel reported that he had been briefly detained by the Munich police after getting into a fight with a nightclub bouncer; no charges were filed.

In Benghazi, the de facto rebel capital in eastern Libya, and in Misurata, a western city that Colonel Qaddafi’s forces have besieged for months, celebratory gunfire rang out and explosions could be heard.

But even then, doubts lingered in Benghazi about whether the news was true: in interviews, residents said they were happy but suspected a ploy by Colonel Qaddafi to win sympathy. Ramadan el-Sheikhy, who said his brother was killed in one of Colonel Qaddafi’s prisons, said any sympathy was misplaced. “I was truly happy at the news,” he said. “Hopefully, he felt the pain of having a relative killed.”

Earlier Saturday, NATO officials had rejected an offer by Colonel Qaddafi to call a cease-fire and negotiate as false. The proposal was delivered in a rambling and often defiant speech, broadcast over Libyan state television, in which Colonel Qaddafi insisted he would never leave Libya.

“Come France, Italy, U.K., America, come, we’ll negotiate with you,” Colonel Qaddafi said. “You lie and say I’m killing my own people. Show us the bodies.”

The speech, which was broadcast at about 2:30 a.m. Saturday, was the latest in a series of proclamations from the Libyan leader, and it was made as NATO forces said they would broaden their list of targets to include palaces, communication centers and other administrative buildings that Colonel Qaddafi relies on to maintain power.