Yusuf al-Qaradawi, viewed as the spiritual leader of the Egyptian opposition Muslim Brotherhood, made the call on Monday through a fatwa (religious decree) against the 42-year-long head of state.
"Whoever in the Libyan Army is able to shoot a bullet at Mr. Gaddafi should do so," he told the Qatar-based news channel al-Jazeera.
Libya has been swept by pro-democracy protests inspired by popular revolutions in Egypt and Tunisia, which toppled the countries' presidents.
Such killing would "rid Libya of him," said Qaradawi. The scholar, who also heads the International Union for Muslim Scholars, returned to Egypt after three decades in exile following the revolution.
Gaddafi's government has deployed fighter jets to open fire on the demonstrators to prevent revolution.
Forces loyal to Gaddafi are also said to have used live rounds against protesters amid reports, pointing to the arrival of planeloads of armed foreign mercenaries in the capital, Tripoli.
Libyan protesters, however, have reportedly managed to seize several cities.
The International Federation for Human Rights says as many as 400 people have so far been killed during the protests.
Qaradawi also told Libyan soldiers "not to obey orders to strike at your own people," and urged Libyan ambassadors around the world to dissociate themselves from Gaddafi's regime.
End item/ 129