Norfolk Police released descriptions of two suspects of Middle Eastern appearance as military personnel were reportedly sent a memo warning them about the incident near RAF Marham on Wednesday.
Detective Superintendent Paul Durham, from the Norfolk and Suffolk Major Investigation Team, 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.
“Visible patrols continue in the area and officers will be carrying out house-to-house enquiries and detailed searches of the scene in Squires Hill, which remains closed for the time being.”
The serviceman in his late 20s, who had been out jogging, has told police he was approached by two men and attacked but he fought them off.
Police say one of the men shouted at the serviceman and attempted to grab him before falling to the ground.
The second assailant, who was armed with a knife, went to his accomplice before they both fled. The men fled in a dark people carrier and remain at large.
The first suspect is said to be aged between 20 and 30, around 6ft tall, of athletic but stocky build, with dark hair which was long on top and a well-groomed beard. He was of Middle Eastern origin in appearance with a dark skin tone and wore dark casual clothing.
The second suspect is described as between 20-30 years old but younger than the first suspect and of a slimmer build. He was approximately 5ft 10, clean shaven with short dark hair. He was also of Middle Eastern origin in appearance and wore a white t-shirt and dark shorts.