Updated 11.45 p.m. -
Prime Minister Lawrence Gonzi this evening told the Libyan deputy foreign minister, Abdul-Ati al-Obeidi, that Col Muammar Gaddafi and his family 'must go'.
Mr al-Obeidi was in Malta as Gaddafi's envoy for talks to bring about a ceasefire in Libya.
The government said that Dr Gonzi told Mr al-Obeidi that Libya must observe all UN resolutions, the Gaddafi government must step down, Col Gaddafi and his family should leave and there should be an immediate ceasefire and a process which would enable the Libyan people to make its democratic choices.
Mr al-Obeidi flew in on a private Cessna jet at about 9.45 p.m. after having had talks with government officials in Greece and Turkey. His meeting with Dr Gonzi, at the Auberge de Castille, lasted for almost an hour.
According to unofficial reports, Obeidi is seeking a way out of the crisis and wants Greece, Turkey and Malta to mediate.
However the Benghazi-based Libyan rebels have already dismissed his proposals.
Italian Foreign Minister Franco Frattini, who spoke with the Greek Foreign Minister after he had talks with Obeidi this morning, said the proposals 'lack credibility' because they ignored the precondition that Col Gaddafi and his family must leave Libya.
"From the Libyan envoy's comments it appears that the regime is seeking a solution," Greek Foreign Minister Dimitris Droutsas said in a statement after his meeting with Obeidi.
A Greek government official said diplomatic efforts included seeking how a ceasefire could be arranged, but described the situation as "very difficult" and said there was "a lot of mistrust on both sides".
The official said Greece was seeking solutions that could "help the first step" and that the "channels of communication" would remain open.
Turkish Foreign Minister Ahmet Davutoglu said before meeting Obeidi that opposition representatives were also expected in Ankara soon.
"We will do our best so that the suffering in Libya comes to an end in the shortest possible time and that a roadmap is outlined in a way that would include political changes in line with the demands of the Libyan people," Davutoglu told reporters.
While Obeidi tried to arrange a ceasefire today, the rebel fighters launched a new attempt to recapture Brega, advancing to the outskirts of the oil refinery town only to be forced back by artillery fire.
Former colonial power Italy announced it was joining France and Qatar in recognising the rebels' Transitional National Council (TNC), and said it would send ships and planes to evacuate the wounded from besieged Misrata city.
The New York Times has reported that two of Gaddafi's sons were offering to oversee a transition to a constitutional democracy that would include their father's removal from power.
But the rebels swiftly rejected any deal involving the Gaddafi family.
"Gaddafi and his sons have to leave before any diplomatic negotiations can take place," TNC spokesman Shamseddin Abdulmelah said.
He said the regime had lost any right to talk of a negotiated exit after it continued to pound Misrata, 214 kilometres (132 miles) east of Tripoli.
Rebels there have again pleaded for support from the international coalition to counter the heavy artillery of Gaddafi's forces who have bombarded the city for more than a month.