But following a barrage of early morning Iranian missiles, Israel reopened its airspace for six hours on Sunday to bring back those stranded abroad since the conflict with Iran began on June 13.
Website Safe Airspace said the US attacks on Iran may increase risks to US operators in the region.
"While there have been no specific threats made against civil aviation, Iran has previously warned it would retaliate by attacking US military interests in the Middle East - either directly or via proxies such as Hezbollah," Safe Airspace said.
Meanwhile, flight tracking website FlightRadar24, said airlines maintained flight diversions around the region.
Its website showed airlines were not flying in the airspace over Iran, Iraq, Syria and Israel. They have chosen other routes such as north via the Caspian Sea or south via Egypt and Saudi Arabia, even if these result in higher fuel and crew costs and longer flight times.
Since Israel launched strikes on Iran on June 13, carriers have suspended flights to destinations in the affected countries, though there have been some evacuation flights from neighbouring nations and some bringing stranded Israelis home.
Safe Airspace said it was possible airspace risks could now extend to countries including Bahrain, Kuwait, Oman, Qatar, Saudi Arabia and the United Arab Emirates. "We continue to advise a high degree of caution at this time," it said.
A spokesperson for Israel's airports authority said the country's main airport, Ben Gurion near Tel Aviv, was expected to reopen for rescue flight landings on Sunday.
Flag carrier airline El Al, along with Arkia, Air Haifa and Israir said they would operate at least 10 flights.
Tens of thousands of Israelis are stuck abroad.
At the same time, nearly 40,000 tourists in Israel are looking to leave the country, some of whom are going via Jordan's borders to Amman and Aqaba and others via Egypt and by boat to Cyprus.
Japan's foreign ministry said on Sunday it had evacuated 21 people, including 16 Japanese nationals, from Iran overland to Azerbaijan. It said it was the second such evacuation since Thursday and that it would conduct further evacuations if necessary.
New Zealand's government said on Sunday it would send a Hercules military transport plane to the Middle East on standby to evacuate New Zealanders from the region.
