Scotland's 12 Premier League clubs agreed on Monday to punish any club whose fans show support for guerrilla groups as they toughened up their rules on 'unacceptable conduct' at league matches.
In a statement on their website, the SPL said they were acting "as part of football's commitment to protect and maintain the good reputation of the game in Scotland."
The move follows a series of incidents this year.
Celtic, the 42-times Scottish champions, were last week fined 15,000 euros by European football's governing body UEFA after their fans sang pro-Irish Republic Army (IRA) chants at a Europa League match against Rennes of France on November 3.
Earlier this year Celtic's arch-rivals Rangers were fined 40,000 euros by UEFA and their fans banned for one away match in European competition for singing sectarian songs at a Europa League match against PSV Eindhoven. It was the fourth time in five years that Rangers had been cited by UEFA.
The SPL said: "The definition of 'unacceptable conduct' within the SPL Rules has been extended to include 'using words, conduct or displaying any writing or other thing which indicates support for, or affiliation to, or celebration of, or opposition to, an organisation proscribed in terms of the Terrorism Act 2000.'"
The SPL have also voted to allow requests from clubs to pilot safe standing areas at SPL matches.
"Since I joined the SPL in 2009, there has been widespread support amongst fans to re-introduce safe standing areas," said SPL chief executive Neil Doncaster.
"I am delighted that we have been able to respond positively to supporters' views on improving the match day experience.comments