James Mellor ruled at the High Court in London in March that 53-year-old Craig Wright was not the mythical figure credited with first launching the cryptocurrency in 2008, following a five-week trial.
The Crypto Open Patent Alliance (COPA), a non-profit organisation set up to keep cryptocurrency technology free from patents, had sued Wright.
He has claimed since 2016 that he was Satoshi Nakamoto and insisted he was the author of a white paper that unveiled what would grow to be the world's most popular cryptocurrency.
Now, in a further ruling, Mellor said he will refer "relevant" papers in the civil legal action to the Crown Prosecution Service (CPS) to consider whether criminal charges should be filed against Wright.
"In advancing his false claim to be Satoshi through multiple legal actions, Dr Wright committed 'a most serious abuse' of the process of the courts of the UK, Norway and the USA," he stated.
The judge had "no doubt" the CPS should consider charges for "perjury and forgery of documents and/or whether a warrant for his arrest should be issued and/or whether his extradition should be sought from wherever he now is".
"All those matters are to be decided by the CPS," Mellor noted.
The CPS, a public body that decides on criminal charges in England and Wales, declined to comment.
It is understood the agency had noted the judge's remarks and could ask police to investigate further if prosecutors believe offences may have occurred.
In Mellor's March decision, he comprehensively dismissed Wright's claims to be Satoshi Nakamoto, calling the evidence against him "overwhelming".
In Tuesday's ruling, the judge granted two injunctions against Wright preventing him from threatening or commencing legal action of a similar type.
He also said that Wright should publicise the details of the ruling made against him "in order further to dispel residual uncertainty".
Wright will have to display a notice on the homepage of his website for six months, with the same notice pinned to his profile on X, and his Slack channels for three months.
