West Yorkshire Police Chief Constable Dee Collins said yesterday's brutal attack on the 41-year-old as she went to meet constituents in northern England appeared to be "an isolated, but targeted attack on Jo".
A 52-year-old man, who has been named by British media as local Thomas Mair, was arrested shortly after Cox was shot and stabbed numerous times in the street.
In a statement, Collins said detectives involved in the murder investigation, which is being aided by counter-terrorism specialists, were "keeping an open mind".
"We are also aware of the inference within the media of the suspect being linked to right-wing extremism which is again a priority line of enquiry which will help us establish the motive for the attack on Jo."
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She added: "Based on information available at this time, this appears to be an isolated, but targeted attack upon Jo -- there is also no indication at this stage that anyone else was involved in the attack.
Eyewitnesses said that Cox was shot two or three times before being stabbed as she lay on the pavement.
Police confirmed she was attacked with a firearm and a knife after driving up to the library in the village of Birstall for a scheduled meeting with constituents.
A 77-year-old man tried to help her and in turn sustained a "serious injury to his abdomen".
He is currently in a stable condition in hospital, Collins said.
Police have up to 96 hours to question the suspect before they must charge or release him, according to government guidelines for serious crimes such as murder.
Collins said this was one of two unrelated incidents involving "Jo receiving a malicious communication of a sexual nature at her parliamentary office in Westminster".
The second case remains unsolved.