Live updates: Follow the latest news on Israel-Gaza
The US has increased efforts to get its citizens out of Israel by chartering a cruise ship from the port city of Haifa.
But US citizens in Gaza remain trapped in the besieged territory as Israel prepares for a ground incursion.
The State Department has arranged several evacuation flights from Israel, and Florida has organised at least one charter flight to the southern US state under an initiative led by Florida Governor Ron DeSantis.
A Department representative on Monday said at least 1,000 Americans have left Israel on US-backed travel since Friday.
The US embassy in Israel on Sunday urged American "citizens and their immediate family members with a valid travel document" to depart from Haifa on Monday.
Cypriot Foreign Ministry spokesman Theodoros Gotsis said the ship's arrival was expected on Tuesday.
"Cyprus has received 26 requests from 26 different countries to act as an evacuation hub and the government is responding to the best of its ability," Cypriot government spokesman Konstantinos Letymbiotis told AFP
The first US State Department-organised charter flight taking Americans out of Israel landed in Athens last week, the Biden administration confirmed on Friday.
US airlines increased connecting flights to help people fly home from Greece.
Commercial options are available but many flights are sold out for days.
More charter flights are scheduled between Athens and Tel Aviv until at least October 19, Reuters reported.
Almost 300 Americans were flown from Israel to Florida after Mr DeSantis signed an executive order to have a state agency conduct the flights.
Mr DeSantis is running for the Republican nomination in the 2024 US election, although he remains far behind former president Donald Trump.
Some sceptics accused him of organising the flight as a political stunt.
Mr DeSantis earlier claimed that the US should not accept Palestinian refugees from Gaza, claiming they "are all anti-Semitic". He travelled to Israel in April.
The US has been in talks with regional partners to help Americans in Gaza leave the besieged enclave through the Rafah border crossing with Egypt, although those efforts have yet to succeed.
