Scottish FA chief executive Stewart Regan says it is time "for clubs to think" about a change to how the football authorities can deal with misbehaving supporters.

The governing body are investigating incidents at Celtic's Scottish Cup tie with Stranraer on Sunday, at which flares were thrown onto the pitch and away supporters were alleged to have sung sectarian songs.

The Scottish Professional Football League is also considering a delegate's report of offensive chanting by Rangers supporters at their Championship game with Hibernian at the end of December. Flares have also been seen at other Scottish football grounds throughout the season.

At present, clubs generally avoid sanction if it can be proven they took necessary measures to prevent what is termed as unacceptable conduct taking place.

But in the light of the recent incidents, Regan wants clubs to think again about implementing a system which would see stricter sanctions against clubs, in the hope it would act as a deterrent to fans.

"There's more of an appetite for more stringent rules because I think there's a recognition that we just can't allow such behaviour to continue," he said. "Quite what that looks like, and how the rules can be amended, will be up to our lawyers to assist us with and also our members' willingness to change.

"At the end of the day, throwing flares is totally unacceptable within Scottish football or indeed football generally. Flares are dangerous, they are life threatening and it's really idiotic to indulge in this behaviour.

"We've started an investigation ourselves. Obviously until the results of that investigation it's difficult to comment on what will happen next but it's got no place in Scottish football.

"We are obviously the custodians of the Scottish Cup so we do have a rule that covers unacceptable conduct and if there's a case then our Compliance Officer can put that case before an independent panel. The panel would consider whether or not sanctions are relevant.

"A few years ago we tried to introduce the concept of strict liability into our rules. That was defeated by our members.

"I think clubs need to think about whether they want such behaviour taking place within Scottish football grounds. Flares are life-threatening, dangerous and they've got no place in Scottish football. Anything we can do to stamp them out I would be very, very supportive of.

"We are about to start the rules revision process for 2016 and, given the events of the weekend and obviously incidents of singing in previous weeks as well, I think it will be back on the agenda for discussion. Quite how far it goes will depend on the members and the appetite for change."

Prominent anti-sectarian charity Nil by Mouth want the game's governing bodies to push for the implementation of the European-standard disciplinary code which would see clubs receive sanctions when offensive behaviour is committed at grounds.

Known as strict liability, the UEFA system automatically results in charges against clubs when there is evidence of fan misbehaviour. Sanctions range from fines to stadium closures in an attempt to act as a deterrent.

Scottish clubs have previously voted emphatically against introducing such a system here.

But the organisation have now written to the Scottish FA and clubs to say the matter must be on the agenda at their annual general meeting this year.

"The vast majority of fans who go to games in Scotland are decent people and are fed up to the back teeth with this behaviour and we want to find a way of ensuring that their voices are heard on this important issue," Nil by Mouth's campaign director Dave Scott told STV.

"That is why we have written to the Scottish FA and SPFL urging them to put strict liability on the agenda for the AGM in June.

"By doing so publicly, they give clubs several months to have meaningful dialogue with their fans about what course of action to take.

"This is too big a decision to simply leave to officials and it's vital that fans are fully engaged in the debate. It's their game and this can be a chance to help clean it up.

"UEFA have been operating strict liability successfully for years and by having a genuine debate on these proposals Scottish football has a chance to stand up to be counted and bring the game into the 21st century.

"The choice for clubs is stark remain part of the problem or be part of the solution."

On Monday, the Scottish FA and Police Scotland started investigations into alleged sectarian singing and the use of pyrotechnics by Celtic supporters at their Scottish Cup match with Stranraer.

Celtic identified and suspended three supporters on Monday for the use of flares at Stair Park and hit out at those responsible.

"[Sunday]'s events have again caused embarrassment to Celtic and our supporters," the club said in a statement.

"On numerous occasions Celtic has stated its strong opposition to the use of pyrotechnics but regrettably again, a very small number of individuals, within a ticket allocation of 2,500, have damaged the club.

"We should be very clear. Those responsible simply do not care about our club, our reputation or the safety of our fans and we do not want them at our matches. The club will be reviewing its ticket allocation procedures to ensure that this matter is addressed.

"Ensuring the safety of our supporters and staff is always of paramount importance to Celtic Football Club. If such behaviour was to continue, the reality is it would only be a matter of time before serious injury is caused. However, we will not allow safety to be compromised by the actions of a tiny minority.

"We have been inundated again by our supporters following yesterdays events and those fans can rest assured that this issue will be dealt with in the strongest terms.

"We cannot and will not allow this minority to destroy the magnificent reputation which our fans have earned over many years."