Ethiopian Airlines Flight ET409, which was carrying 90 passengers of mostly Lebanese and Ethiopian descent, took off from Beirut airport early on Monday headed for the Ethiopian capital Addis Ababa.
The plane apparently broke up in the air before crashing into the sea during a thunderstorm.
Ghazi Aridi, the Lebanese transport minister, said on Tuesday that it was too early to draw any conclusion on pilot error, but the Ethiopian Airlines Boeing 737-800 plane made a sharp turn before disappearing off radar screens and plunging into the sea.
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"The control tower asked him to go in a certain direction, but the pilot was not responsive, then communication was cut off and the plane disappeared off the radar," Aridi said.
"Nobody is saying the pilot is to blame for not heeding orders," he said, adding: "There could have been many reasons for what happened … Only the black box can tell."
Rescue teams have recovered pieces of the plane, but hopes of finding any survivors have faded.
At least a dozen bodies have been recovered so far but there were conflicting reports on exactly how many.
At Beirut's government hospital on Wednesday, health officials handed over to families the remains of two victims who were identified using DNA, Mohammed Jawad Khalife, the health minister, said.
Three other victims, two of them toddlers, also have been identified so far, the minister said.