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.