Ethiopian Airlines Flight 409 lost contact with Beirut airport shortly after takeoff at 02:37 am (0037 GMT) and crashed into the Mediterranean 2.5 nautical miles off the coastal town of Naameh, south of the airport, in stormy weather.
"Three minutes after takeoff, the control tower lost contact with the aircraft. The cause of the crash is as yet unknown, but intensive search efforts are still under way," Information Minister Tarek Mitri told reporters.
He ruled out foul play.
"All those involved say there is nothing that indicates an act of sabotage," he said, echoing comments by President Michel Sleiman and Defence Minister Elias Murr who said it appeared the storm was to blame.
Murr said later that the plane failed to follow instructions from Beirut air traffic controllers for unknown reasons.
"A command tower recording shows the tower told the pilot to turn to avoid the storm, but the plane went in the opposite direction," the minister said in a television interview.
"We do not know what happened or whether it was beyond the pilot's control," Murr added.
By late afternoon, at least 24 bodies had been recovered, including that of a three-year-old, rescue officials said.
Red Cross volunteers transported 14 bodies and some body parts to the state hospital.
One rescue official told AFP that some victims had been dismembered.
"The bodies found were apparently of passengers who did not have their seat belts on and who floated to the surface," he said on condition of anonymity.
"Divers are working to recover the bodies of those who had their seat belts on and sank to the bottom of the sea."
At the hospital, where anguished family members awaited news, grim-faced officials played down hopes of anyone being found alive.
"We do hope but it's unlikely," Health Minister Mohammed Jawad Khalifeh told reporters. He said the ministry had set up a crisis unit to identify victims through DNA tests or personal belongings.
Luggage and debris from the Boeing 737, which had been bound for Addis Ababa, washed up south of Beirut during the day.
Empty seats, gift-wrapped children's toys and even a coffee machine from the plane were found near the airport, an AFP correspondent said, adding that soldiers were dragging metal pieces of debris along the shoreline.
Witnesses reported seeing flames as the plane plunged into the sea in "a huge ball of fire".
Relatives of passengers, some weeping uncontrollably, huddled at Beirut airport's VIP lounge and at the state hospital to await news.
Sleiman, Prime Minister Saad Hariri, parliament speaker Nabih Berri and ministers and deputies rushed to comfort them.
"We are working with all the power we have to try and find missing people from this tragedy," Hariri said from the airport. "We are working to find the black box that will tell us what really happened on the plane."
Later he chaired an emergency meeting with officials including Murr, Khalifeh, army commander Jean Kahwaji and police chief Ashraf Rifi.
The Lebanese army, navy, the United Nations Interim Force in Lebanon (UNIFIL) and aircraft from France, Britain, Cyprus and the United States were all assisting in rescue efforts, officials said.
An American destroyer, the USS Ramage which specialises in rescue operations, arrived on site at 4:00 pm (1400 GMT), a US embassy spokesman said.
The Ethiopian News Agency in Addis Ababa said Ethiopian Airlines sent a team to Beirut to investigate the crash.
Officials said 83 passengers and seven crew members were aboard the doomed flight.
The passengers included 54 Lebanese, 23 Ethiopians, one French woman, one Briton, one Iraqi, one Syrian, one Turk and another of as yet undetermined nationality.
The French passenger was identified as Marla Sanchez Pietton, wife of Paris's ambassador to Lebanon Denis Pietton, the French embassy told AFP.
Three Lebanese passengers had dual nationality, from Britain, Canada and Russia.
The Boeing 737-800 entered commercial service in 1998 and is one of the latest versions of the world's most widely used short- to medium-haul airliner, capable of carrying 189 passengers.
Ethiopian Airlines, established in 1946 and operating an all-Boeing fleet, is considered one of Africa's best carriers, but has had two major crashes since 1980.
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