Leader Muammar Gaddafi and his sons appear to be looking for a way out of the conflict in Libya.
Western forces led by the United States, France and Britain began air attacks on government troops on 19 March in order to enforce a United-Nations-sanctioned no-fly zone and protect civilians. NATO assumed responsibility for the military operation last week.
Greece's foreign minister said after a meeting in Athens between the prime minister and a Libyan envoy that Colonel Gaddafi's regime is looking for a solution.
The New York Times is reporting that at least two of Colonel Gaddafi's sons are proposing a transition to a constitutional democracy that would include their father's removal from power.
The Pentagon announced on Sunday that the US involvement would continue on Monday at NATO's request, because of "recent poor weather in Libya".
Meanwhile, hundreds of wounded people in besieged Misrata have been evacuated on Turkish aid ship the Ankara.
They told of a city that has gone weeks without electricity or running water, where snipers have emptied the centre, and mortar rounds and rockets rain down at random on residents huddled inside their homes, AFP reports.
Doctors on the vessel said many people had extremely serious injuries and medical care conditions in Misrata were inadequate.
The Ankara is sailing for the Turkish port of Cesme.