The most significant news doing the rounds in Libya and internationally Tuesday was the suggestion that the Libyan leader, Muammar Al Qathafi could call it a day and leave the country within three days without getting pursued by the Libyans for crimes committed. But at the end of the day the Libyan people still harbour doubts as to what could happen.

Mustafa Abdel Jalil, the head of the National Libyan Council told Al Jazeera that they first heard about such a proposal made on television “to the wise men of the country in order to reach a solution to put an end to the bloodshed namely on the areas of Misurata, Az Zawiyah and Ras Lanuf.”

He went on to say that based on their integrity and their love to the country, the Council proposed that a solution could be reached under three key demands, namely, that all bombardments are stopped, that Al Qathafi departs the country within 72 hours, and as such they would waive their right of prosection domestically for the crimes of oppression, persecution, starvation and massacres.

Abdel Jalil said that Al Qathafi's men did not come with a clear proposal. “They came with a suggestion and asked for the guarantees and assurances on our part in ending the bloodshed. He said the proposal was made on state television by Jadallah Azous Al-Talhi, a Libyan prime minister in the 1980s and a leading member of Libya's ruling establishment.

Asked if the Council could offer Al Qathafi immunity from prosecution if the international Criminal Court is going to be involved, Abdel Jalil said that don't have the authroity to speak on behalf of others. “We are speaking of the Libyans only. We can waive the right of prosecution domesticallyfor the crimes in Libya of oppression and massacres, particularly at Abu Slim.

He went on to say that Al Qathafi's people have not proposed any solutions after their suggestions.

Libyan state television Tuesday denied reports that the Libyan leader tried to strike a deal with opposition forces seeking his removal, with an official from the Libyan foreign ministry describing the reports as "absolute nonsense".

However, Jalil said they had the conviction that any official appearing on state television cannot make such a statement without getting the green light from the Libyan leader himself.

"We will have to wait and see what the regime's response is," Abdel Jalil said.

In the meantime, Al Qathafi security forces continued to strengthened their military position, squeezing rebel-held towns in the west and checking the advance of rebel militias westwards towards the capital, Tripoli.

Tuesday reports saud that Al Qathafi forces used tanks and aircraft to attack the town of Az Zawiyah, 50 km west of Tripoli, but rebels were quoted saying they still control the town centre.

Fighting is also intensifying in Ras Lanuf amid reports of several air strikes on Tuesday and families residing were seen heading eastward in an apparent attempt to flee the fighting in that town. There were a nmber of causualties.

The regime's forces have reportedly continued to move eastward in an effort to push the rebels back and recapture fallen towns.

On Tuesday a senior Red Crescent official said forces loyal to AL Qathafi were reported by Al Jazeerablocking migrant workers from crossing into Tunisia, and forcing many to return to work in Tripoli.