Italy, Greece and the Netherlands are sending transport planes to Libya to get their citizens out. Austria and Portugal have already done so.
But Egypt said the runways at Benghazi airport had been destroyed in the anti-government uprising.
UK nationals have been told to take commercial flights from Tripoli.
International oil firms, many of them engaged in major energy projects in Libya, are evacuating expatriate staff.
Royal Dutch Shell said all of its expatriate staff and their dependants had been relocated from Libya.
Italy's Eni, the biggest foreign energy producer in Libya, said it was evacuating some of its expatriate staff. French oil firm Total and construction firm Vinci said they were doing likewise.Continue reading the main story Colonel Muammar Gaddafi has led since 1969Population 6.5m; land area 1.77m sq km, much of it desertPopulation with median age of 24.2, and a literacy rate of 88%Gross national income per head: $12,020 (World Bank 2009)Turkey is sending two ferries to Benghazi to evacuate its citizens. The offices of 14 Turkish construction firms were looted during the unrest, a Turkish minister said, though no casualties were reported in those incidents.
Foreign Trade Minister Zafer Caglayan told reporters in Ankara that about 4,000 Turkish workers were employed at construction sites in the Benghazi, Darnah and Tobruk areas.
In all, about 25,000 Turks are working for more than 200 Turkish construction firms in Libya, he said. The contracts are worth $27bn (£17bn) in total, he added.
Russia says it also plans to start evacuating its nationals on Tuesday. More than 500 Russians are working in Libya, including many building a high-speed railway line.
Brazil says it is trying to get permission to land a plane in Libya to evacuate 170 people from Benghazi. Up to 600 Brazilians are working in Libya.
The UK Foreign and Commonwealth Office says Libyan officials are letting foreigners leave without exit visas.
On its website the FCO says: "Commercial flights are available from Tripoli airport. However, the majority of airport offices in Tripoli are closed until further notice.
"We advise British nationals who wish to leave Libya but cannot purchase tickets online to travel to the airport carrying sufficient cash to buy tickets."
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