Al Jazeera's correspondent in Beirut, Rula Amin, said search-and-rescue efforts were being hampered by adverse weather conditions.
"The ships trying to help do not have an easy task .. the weather is stormy, with strong winds, heavy rains and high waves," Amin said.
In the past two days, many parts of Lebanon have suffered harsh wintry storms that have caused heavy flooding and damage in some parts of the country.
UN peacekeepers based in Lebanon have joined the search.
"[The crash] site has been identified three and a half kilometres west of the [coastal] village of Naameh," Ghazi Aridi, the Lebanese transport minister, said.
The aircraft carried 54 Lebanese nationals, 22 Ethiopians, as well as Iraqi, Syrian, British and French nationals, he said.
Thousands of Ethiopians work as domestic helpers in Lebanon.
There were also several dual nationals including one British-Lebanese, one Canadian-Lebanese and a Russian-Lebanese.
Hoping for news
Our correspondent said relatives of some of those on board the flight had gathered at Beirut airport hoping for news.
According to the Ethiopian Airlines website, the flight from Beirut bound for Addis Ababa is operated by a Boeing 737 aircraft.
|Helicopters and UN forces in Lebanon joined the search and rescue operation [Reuters]
The flight had been scheduled to depart from Beirut at 02:10am, landing at Addis Ababa at 7:50am local time.
The 737 is the world's best-selling commercial passenger aircraft and more than 6,000 have been sold or ordered since the aircraft was first introduced in 1967.
The Ethiopian News Agency in Addis Ababa said Ethiopian Airlines had sent a team to Beirut to investigate the crash.
Saad Hariri, the Lebanese prime minister, declared Monday a national day of mourning, as the government cancelled a scheduled cabinet meeting.
Michel Suleiman, the country's president, described the incident as "painful" and called on Lebanese hospitals to be on alert.