The head of the rebel group National Libyan Council told al-Jazeera the deadline will not be extended, The Washington Post reported.
"If he leaves Libya immediately, during 72 hours, and stops the bombardment, we as Libyans will step back from pursuing him for crimes," council leader Mustafa Abdel Jalil told al-Jazeera.
"Conditions are that firstly he stops all combat in the fields; secondly that his departure is within 72 hours; thirdly we may waive our right of domestic prosecution ... for the crimes of oppression, persecution, starvation and massacres."
Spokesmen for both the Gadhafi government and the opposition forces said Tuesday reports Gadhafi was negotiating with the rebels about stepping down were false, the Post reported.
Fighting between the insurgents and forces loyal to Gadhafi were unabated Tuesday.
Libya has been in the throes of a weeks-long clash between rebels and government forces as the country descends into civil war. The protests against Gadhafi began Feb. 15 as anti-government demonstrators sought the ouster of Gadhafi, 68, who has ruled for more than four decades.
Death toll estimates range from more than 1,000 to as many as 2,000. Tens of thousands more have fled the country.
"Both the Libyan government and opposition forces need to allow unhindered access for aid organizations to assist civilians," Bill Frelick, refugee program director at Human Rights Watch, said Tuesday. "People living in areas of heavy fighting in western Libya are now in dire need of medical aid and other assistance."
As reports of possible negotiations circulated, the Libyan government pursued its air assault near Ras Lanuf's oil refineries against anti-government rebels to drive them further east, witnesses said.
The government said the air attacks injured a family of five, The New York Times reported.
The air attacks have helped negate recent gains by the rebels in their westward move toward Tripoli.
The elite Khamis Brigade maintained its pressure on opposition-held Zawiyah, west of Tripoli, using tanks, artillery and snipers, a witness told the Times. She said heavily armed government troops attacked Monday morning then withdrew for unknown reasons.
Government forces also attacked the rebel-held city of Misurata, about 100 miles east of Tripoli, witnesses said.
Rebels have rejected any foreign invasion of the country but indicated they would welcome a no-fly zone, the Times reported. British and French diplomats said Monday they would seek U.N. authority for a no-fly zone, but Russia, which has veto power, has dismissed any military intervention.
Ivo Daalder, the U.S. ambassador to NATO, said the military alliance set up 24-hour surveillance of Libya with AWACS reconnaissance aircraft, Stars and Stripes reported.
"The decision was made to indeed increase the surveillance of the NATO-AWACS capability to make it 24/7, to have a better picture of what's really going on in this part of the world," Daalder said during a news conference. "We're looking at all the options that are out there ... . But the most immediate options that are now most available and that we're really looking at is how can NATO support the humanitarian effort that is ongoing by the international community."
The military alliance has been developing plans should Western allies reach agreement on a no-fly zone. The ministers will meet in Brussels Thursday to discuss options to address the situation, Stars and Stripes said.
Libyan Foreign Minister Musa Kusa, during a news conference in Tripoli, accused the United States and Britain of "yearning for the colonial era" and trying to divide the country. He said about 300 al-Qaida fighters once held by the United States at Guantanamo Bay, Cuba, backed rebel forces, a variation of a theme Gadhafi has espoused about the anti-government protesters.
"They are now fighting in eastern Libya. Their methods and approaches are clear," Kusa said. "When they were released, they started moving again, and they have taken weapons."
Notable deaths of 2014 [PHOTOS]