Helicopters and navy vessels rushed to the crash site as President Michel Sleiman ruled out foul play.
Transport Minister Ghazi Aridi said Ethiopian Airlines Flight 409 lost contact with the airport control tower shortly after takeoff and crashed into the Mediterranean sea 2.5 nautical miles off the coastal town of Naameh, south of the airport.
"The control tower was assisting the pilot of the plane on takeoff and suddenly lost contact for no known reason," Aridi told reporters.
Families of the passengers, some of them weeping, could be seen huddled at the VIP lounge of Beirut International Airport while awaiting news of their loved ones.
One woman was sobbing and screaming, "Why, why?" as others fainted and had to be carried away by Red Cross volunteers.
"I know they won't find him," wailed one woman, referring to her husband who was on board the doomed flight.
A government official said there were several children on board the plane, which crashed about five minutes after takeoff at 2:30 am (1230 GMT).
Witnesses reported seeing a ball of fire as the Boeing 737 plunged into the sea.
A defence ministry official told AFP that 10 bodies had been recovered at the crash site by early morning.
Sleiman said authorities had ruled out terrorism or sabotage as the cause of the crash.
"Up until now we have ruled out foul play," Sleiman told reporters.
"This is a painful tragic event. We are sparing no efforts in trying to find survivors," he added.
"Our heartfelt sympathy goes out to the families of those on board."
The Ethiopian News Agency in Addis Ababa said Ethiopian Airlines has sent a team to Beirut to investigate the crash.
The accident took place amid heavy rains and storms in Lebanon in the past two days that have caused heavy flooding and damage in some parts of the country.
Officials listed 83 passengers and seven crew members as having been on board the flight.
Aridi said the passengers include 54 Lebanese, 22 Ethiopians, one Iraqi, one French woman, one Syrian and seven crew members. There were also several dual nationals including one British-Lebanese, one Canadian-Lebanese and a Russian-Lebanese.
Among those on board the flight was Marla Sanchez Pietton, the wife of France's ambassador to Lebanon, Denis Pietton, the French embassy told AFP.
Thousands of Ethiopians are employed as domestic workers in Lebanon and Ethiopian Airlines operates a regular flight between Addis Ababa and Beirut.
Aridi said he had formed an investigative committee to determine the cause of the crash and had contacted nearby countries to assist in the search and rescue effort.
The Lebanese army, navy as well as the United Nations Interim Force in Lebanon (UNIFIL) were assisting in the rescue, Aridi added.
"We have contacted everyone, inside and outside the country, that can assist us and the Lebanese navy, the army and UNIFIL have joined in the rescue," the minister added.
He said the French organisation responsible for technical investigation of civil aviation accidents was taking part in the probe.
A government official said Cyprus was assisting in the search and rescue efforts as were naval vessels from the UN force stationed in Lebanon (UNIFIL).
Prime Minister Saad Hariri declared Monday a national day of mourning, as the government cancelled a scheduled cabinet meeting.
The Boeing 737-800, which entered into commercial service in 1998, is one of the latest versions of the world's most widely used short to medium-haul airliners, and is capable of carrying up to 189 passengers.
The accident comes just one month after a Panamian-flagged ship transporting livestock capsized in stormy weather and sank off the coast of northern Lebanon with around 80 sailors on board.
The majority of the sailors were rescued but 26 were unaccounted for and presumed dead.
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