Confirming that thousands of refugees have crossed into Tunisia, Red Crescent representative Gerard Lautredou said the numbers could rise in coming hours.
"We're preparing to receive 10,000 people a day along the border with Libya," Lautredou told the BBC.
Reports citing eye-witnesses say that the Libyan military has fired on protesters from helicopters and bombed them from aeroplanes.
The Libyan government is reported to have lost control of much of the eastern part of the country.
Italian foreign minister Franco Frattini on Wednesday dismissed Libya's official number of 300 dead during a week of protests, putting the death toll at 1,000 - the same figure used by reports citing eye-witnesses in the north African country.
An Arab member of the International Criminal Court interviewed by al-Arabiya put the death toll at 10,000 with more than 50,000 injured.