Israel has vowed to annihilate the Hamas movement that rules the Gaza Strip in retribution for the deadliest attack on civilians in its history when hundreds of Hamas gunmen crossed the barrier and rampaged through Israeli towns on Saturday.

"We flew (to Tel Aviv) on Sunday, we stopped flying on Monday. We're in touch with the airport, there's no engineering cover at the moment. That's being restored today," O'Leary told reporters at a previously scheduled industry briefing in Brussels.

"So we're looking to put back at least one or two daily flights from tomorrow, Friday. The airport wants us to restore a daily flight to Vienna and a daily flight to somewhere else ... but it's subject to the security situation."

Israel has put Palestinian enclave Gaza, home to 2.3 million people, under total siege with no humanitarian exceptions and launched the most powerful bombing campaign in the 75-year history of the Israeli-Palestinian conflict.

Air France-KLM, said its commercial flights had been cancelled but France had organised special evacuation flights.

"The French have authorised that we fly one flight a day on a special exemption from Paris to Tel Aviv starting today and for our regular schedule ... we will not cancel the rest of the month. We are on a 48 hour rolling period," Air France-KLM CEO Ben Smith said.

Lufthansa, and British Airways (BA) parent IAG, were also monitoring events.

IAG said the group had decided to cancel Israel flights until Oct. 14 to see how the situation unfolds after BA diverted a flight on Wednesday due to security concerns.

The British government on Thursday said it would organise flights to get its citizens out of Israel and ordered families of its diplomats to leave in the wake of the war with Hamas. The first flight is expected to leave Tel Aviv on Thursday.

Similarly, Lufthansa CEO Carsten Spohr said it was operating special evacuation flights for the German government.

"We have aircraft in the air now as part of a special operation to evacuate Germans from Tel Aviv ... but we are not taking the decision yet on reopening our commercial flights, (it's) subject to the security," Lufthansa said, adding the German government decides who boards the planes.

(Reporting by Joanna Plucinska and Julia Payne; Editing by Jason Neely and Mark Potter)

By Julia Payne and Joanna Plucinska