Georgios Lillikas, Cyprus' foreign minister, said: "Many countries are seeking our help. We are talking about assisting 60,000 to 70,000 people. It's humanly impossible."
It is the first sign that Cyprus is feeling the pressure from an exodus of thousands of foreigners from Lebanon.
Speaking from the port of Larnaca, the main harbour which has been receiving evacuees since Monday, Lillikas said: "What we need are more planes sent to Cyprus, so people can move on to their countries as soon as possible."
At least five ships were expected to dock in Cyprus on Thursday carrying Europeans and Americans.
The United States said it expected to assist around 6,000 American citizens by Friday, while the UK said around 5,000 of its citizens were leaving Lebanon.
The United States has leased a compound in the island's capital, Nicosia, to provide accommodation for people who may not be able to move on immediately.
Lillikas said: "We have also given 25 schools and other areas to provide hospitality to people, but with such large numbers we may not be able to cope."
He said a request to increase evacuation flights would be submitted to the presidency of the European Union.