Delta Air Lines and American Airlines Group Inc. said they are canceling flights to Israel until further notice after reports that a rocket landed near Tel Aviv's Ben Gurion Airport.

A Delta Boeing 747 from New York was flying over the Mediterranean headed for Tel Aviv on Tuesday when it turned around and flew to Paris instead. Flight 468 had 273 passengers and 17 crew on board.

Airlines and passengers are growing more anxious about safety since Malaysia Airlines Boeing 777 flying over eastern Ukraine was shot down last week, killing all 298 people on board.

American Airlines said it cancelled its Philadelphia-Tel Aviv flight that was supposed to depart Tuesday night. It also scrubbed its Tel Aviv-Philadelphia flight that was supposed to depart from Israel earlier Tuesday. That plane is on the ground at the airport.

European airlines are monitoring the situation, though still flying. Deutsche Lufthansa AG said its plans are not affected, but will monitor the situation and may cancel flights depending on the situation on the ground.

"We continue to operate as normal. Safety and security are our highest priorities and we continue to monitor the situation closely," a British Airways spokeswoman said.

Ofer Lefler, spokesman for Israel Airports Authority, said the airport is secure.

"We are not talking about a decision of the U.S. government, rather the decisions of two airlines. Delta and US Air, independently, have canceled flights due to arrive in Israel this evening," Mr. Lefler said in a statement.

"The ministry of transportation and civil-aviation authorities have told the airlines that Ben Gurion is secure for takeoffs and landings," he continued.

Discount carrier EasyJet PLC, Europe's second-largest, still serves Tel Aviv "as no government advice has changed on travel to the region," the airline said. "We are allowing passengers booked on that route to change their dates or destination if they wish to," it said. Air Berlin PLC is adopting the same policy as EasyJet.

Write to Susan Carey at susan.carey@wsj.com and Robert Wall at robert.wall@wsj.com

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