Alexander's helmet was damaged; a second strike would certainly kill him.
In all, the two strikes killed 19, including a child, and wounded around 140.
A senior military official said the strike killed "a few" of the fighters, while the others fled.
"Sometimes they have to wait, because the strike doesn't kill right away."
Both sides have said a strike will probably kill the airline.
They said an attempted strike on him last month killed his wife and children.
Local sources say the strike killed a family of six, including four children.
The strikes reportedly killed 30 militants and wounded 40 others.
The strike killed three Chinese and wounded at least 20 others.
The American military opened an investigation into the attack after people in the area said the strike had killed members of a wedding party.