It said three flights had already been chartered to help British nationals leave.
The number of people telling the UK government they are in Lebanon should be treated with caution because British nationals do not have to register their presence there.
“Based on our contacts so far, we also anticipate that only a fraction want to leave due to their strong ties in the country,” the Foreign Office added.
Neighbouring Israel began a ground invasion of Lebanon this week in its battle with the country’s powerful Hezbollah militant group.
It has bombed Hezbollah targets in the capital Beirut.
British nationals and their spouse or partner, and children under the age of 18, are eligible, external to take the new chartered flight, with vulnerable people a priority.
As of last month, there were thought to be between 4,000 and 6,000 UK nationals, including dependants, in Lebanon.
Some have been able to leave on commercial flights but said empty seats were hard to find.
The Foreign Office earlier said it was working to increase capacity on commercial flights for British nationals, and that around 700 troops and government staff had been deployed to Cyprus for “contingency planning”.
Prime Minister Sir Keir Starmer urged British nationals still in the country to come forward to be evacuated, saying: “Now is the time to leave, we have got the plans in place.”
Foreign Secretary David Lammy said: “The situation in Lebanon remains volatile, so I am glad that we have helped the many people who have heeded our advice to leave the country immediately.
“With demand falling, and the security situation deteriorating, there is no guarantee other options to leave quickly will become available. I urge anyone who wants to leave to register now.”
