Israeli security sources say they have received more than 50 warnings of possible attacks in the holiday period.
The three were said to have watched the explosion and then left the airport, according to security sources.
A Malian security source put the number of dead fighters at 60.
Palestinian security sources and witnesses said more than 50 soldiers had been involved in the operation.
Lebanese security sources said that the three were Hezbollah members.
According to a security source, the fighting took place on the highway leading to the airport and had to be closed for one hour.
"He has problems, big problems," an Israeli security source said.
A senior security source last night admitted that the gun's recovery was now an even greater priority.
An Israeli security source said there was a "targeted operation" in the area, but gave no further details.
Earlier, security sources said 12 people had been detained.