Police are still trying to trace two men after the attempted knifepoint abduction of an RAF serviceman.
The married serviceman, who is in his late 20s, was out running near RAF Marham, in Norfolk, on Wednesday when he was grabbed by a man, who tried to drag him towards a nearby car.
He knocked the first attacker to the floor and an accomplice, carrying a knife, helped him up before both men fled.
The serviceman was said to have been left "very, very shaken by his ordeal".
Norfolk Police Detective Superintendent Paul Durham said that there may have been an element of "pre-planning" and that police cannot rule out terrorism as a motive.
He said: "I can confirm we are treating this as an attempted abduction and detailed inquiries are being carried out at the scene to establish the full circumstances.
"The motivation for the attack remains unclear at this time, and whilst we are currently unable to discount terrorism, there are a number of other possible hypotheses. We are therefore carrying out a thorough investigation to understand what has happened, why and who is responsible."
When asked at a press conference if he thought it was a pre-planned attack, Mr Durham replied: "I would be speculating at the moment but it is difficult to envisage a situation where perhaps there wasn't an element of pre-planning, but it's too early to say for sure."
He added: "It was a regular running route for the victim, it's a regular running route for a number of personnel within RAF Marham, it's a well-trodden path."
Police are keen to trace the two men, a dark-coloured people carrier and also the "military-style" knife, with a two-and-a-half to three-inch blade.
Mr Durham said it was believed the first man shouted something at the victim, who did not hear what he said because he was listening to music.
Norfolk Police released descriptions of two suspects of Middle Eastern appearance as military personnel were reportedly sent a memo warning them about the incident.
The first suspect is described as between 20 and 30 years old, about 6ft tall, of athletic, stocky build, with dark hair which was long on top. He had a well-groomed beard, was of Middle Eastern origin in appearance, with a dark skin tone and he wore dark casual clothing.
The second suspect is described as being between 20 and 30 but younger than the first suspect and of a slimmer build. He was approximately 5ft 10in tall, clean-shaven, with short dark hair. He was also of Middle Eastern origin in appearance and wore a white t-shirt and dark shorts.
Military bases were increasingly vigilant after the incident although the threat to the public remains unchanged, police added.
A note seen by the Daily Mirror and addressed to all service personnel in the wake of the incident warns: "2x Asian males approached a serviceman who was running approximately 1 mile outside of RAF Marham main gate and tried to bundle him into their vehicle.
"The vehicle was a dark-coloured Ford Galaxy. The Asian males were carrying a knife when the serviceman was approached."
A further memo advised military staff to keep a low profile and not to be alone on foot or on a bicycle in any uniform or clothing which identifies them as being with the forces.
An RAF spokesman and Norfolk Police refused to comment on the statement.
Detectives have set up a dedicated hotline appealing for information - particularly from witnesses who saw a dark coloured people carrier in the King's Lynn area on Wednesday afternoon.
Anyone with information should call 0800 056 0154 or 0207 158 0011.