Scottish Dawn is facing a ban under UK terror laws after a similar group founded shortly before it called National Action was classified as a terrorist organisation by Home Secretary Amber Rudd.
It became the first domestic group to be outlawed under the legislation.
National Action members provoked controversy after they openly celebrated Ms Cox’s murder in June 2016 at the hands of Scottish-born far right extremist Thomas Mair.
ITN News has revealed Scottish Dawn is now facing a ban.
On its website, the group describes itself as “a patriotic society for the defence of our race and nation active across Scotland”.
Scottish Dawn first came to prominance when they demonstrated against the housing of refugees in Scotland in March.
The group has been under investigation since the demonstration in Alloa where its nembers waved yellow flags bearing a black symbol called the ‘life rune’ - which also appeared in Nazi propaganda.
A ban would mean anyone supporting or attempting to join the group would face criminal charges.
The Head of Police Scotland’s Organised Crime and Counter Terrorism Unit, Detective Chief Superintendent Gerry McLean, told ITN: “National Action is the first domestic extremist group to have been prescribed by the Home Sectreary and there is no place in Scotland for these types of extreme right-wing views.
“Where we identify instances of new groups or individuals who have broken away from National Action we will work with partners and our communities to target and disrupt those involved.”