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“Any solution for the future of Libya has a precondition: that Gadhafi’s regime leaves; that Gadhafi himself and the family leave the country,” Mr. Frattini said.

The provisional Interim National Transitional Council denounced the latest Gadhafi proposal as “unacceptable, as is any policy initiative that does not lead to the end of the Gadhafi regime,” Mr. Issawi said.

A source close to the opposition also said the opposition will never settle for a plan that keeps members of the regime in power.

“There will be no going back at this point. Too much blood has been spilled,” she told The Times on the condition of anonymity.

Western officials are also interested in signs of fissures in the military, although one source described the difficulty of gauging the extent of the military’s loyalty to the Gadhafis.

The resistance doubts that Col. Gadhafi has any interest in a real cease-fire because his troops have escalated their offensive on rebel-held cities, members of the opposition said Monday.

Misurata, 130 miles east of Tripoli, was the scene of heavy fighting Monday, as pro-Gadhafi forces used tanks and snipers to gain control of the city, which has been under siege for more than 40 days.

Mohamed, a rebel spokesman whose full name has been withheld out of concern for his safety, said Misurata was on the brink of a humanitarian crisis.

Some defectors remain fearful of the regime, even in self-imposed exile.

A senior official who defected after the uprising began told The Times that he will not publicly call for Col. Gadhafi to step down because he still has relatives in Libya.

“I have a big family. Not all of them are with me,” the defector said on the condition of anonymity.

“Some of the people who are left around him may be waiting for an opportunity to take Gadhafi out. But they know that if they do it now, it could be suicidal,” said the opposition source.

Ben Birnbaum contributed to this article, which is based in part on wire service reports.