The United Nations peacekeeping operation in Lebanon has sent three ships and two helicopters, and a British RAF helicopter is also involved.
Lebanese soldiers are also combing nearby beaches, where pieces of the plane and debris including passenger seats, a fire extinguisher and bottles of medicine have washed up.
The BBC's Will Ross in Nairobi says the crash is likely to invite comparisons with the Kenya Airways crash in Cameroon in 2007, in which 114 people died.
Both incidents involved Boeing 737-800 aircraft taking off in bad weather.
Relatives of the passengers, some of them sobbing, gathered in the airport's VIP lounge.
A tearful Andree Qusayfi told the Associated Press that his brother, 35-year-old Ziadh, had left for Ethiopia to work for a computer company.
"We begged him to postpone his flight because of the storm," he said. "But he insisted on going because he had work appointments."
Lebanese Prime Minister Saad Hariri, parliament speaker Nabih Berri and other officials went to comfort families.
Both Ethiopia and Lebanon have declared a national day of mourning.
Ethiopian Airlines operates a regular flight between Addis Ababa and Beirut.
Our Nairobi correspondent says that along with South African and Kenya Airways, Ethiopian Airlines is widely considered to be among sub-Saharan Africa's best operators.
And on a continent with a history of national airlines folding often due to reckless financial mismanagement, he says, Ethiopian Airlines is expanding its fleet and was the first African airline to order the Boeing 787 Dreamliner.
It has also just announced the purchase of another 10 737-800s, at a cost of $750m.
Its last major crash was in 1996, when a hijacked Nairobi-Addis Ababa plane ditched into the sea off the Comoros Islands after running out of fuel. Of the 175 people on board, 123 were killed.
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