Israel's airlines said on Tuesday that they had received government permission to start flights to bring back people who had been stranded abroad during the conflict with Iran.
Israel's airspace has been closed since Israel and Iran began trading attacks on Friday, stranding tens of thousands whose flights to Tel Aviv were cancelled.
There would still be no passenger flights leaving Israel, it added. El Al has cancelled all scheduled flights through June 23.
"We understand the difficulty, uncertainty and stress experienced by El Al customers abroad who are seeking to return to Israel, as well as those whose travel plans were disrupted," it said.
"The rescue flights will be operated gradually, and therefore patience is required from El Al customers abroad. We recommend preparing for extended stays and lodging arrangements."
Smaller rival Arkia said it would bring back Israelis from Karpathos in Greece, Larnaca in Cyprus and Tivat in Montenegro.
"Arkia is prepared to operate during any time window approved by the security authorities, including Fridays and Saturdays, and is working with authorities to explore expanding the rescue operation," it said.
Israel's Transportation Ministry has said there are as many as 150,000 Israelis abroad, around 50,000 of them seeking to return to Israel.
El Al said that within 90 minutes of opening a portal for passengers seeking to fly home, more than 60,000 people joined an electronic queue to register.
Cruise operator Mano Maritime, whose "Crown Iris" ship carries 2,000 passengers, said it would make two crossings from Cyprus to Israel's Mediterranean port city of Haifa.
Large numbers have converged on Cyprus, the European Union member state closest to Israel. Flights from the coastal city of Larnaca to Tel Aviv take 50 minutes, and boat crossings to the Haifa take about 15 hours.
Foreign carriers have often cancelled flights during Israel's war against Hamas militants in Gaza, leaving El Al, Arkia and Israir to fill the gap for travellers.
