Thousands of Rangers fans breached lockdown rules last weekend to celebrate the side's first Premiership title in a decade, leading to worries the scenes could be repeated on March 21 at Celtic Park.
Sport Minister Mairi Gougeon and Justice Secretary Humza Yousaf were involved in the talks on Friday alongside representatives from Police Scotland, Glasgow City Council and the two clubs.
Speaking after the meeting, Gougeon said: "This was a positive meeting which we called to address the need for fans to stay at home during the upcoming fixture on March 21.
"The reason we have allowed elite football to proceed is as much for the benefit of supporters as for those working in professional sport.
"Everyone is being deprived of so much right now - and making so many sacrifices - that the ability to watch a football game safely at home on television should be something that people should have the ability to do.
"But a minority cannot be allowed to act irresponsibly. We want to send out a very clear message that all fans must stay at home.
"Clubs have a leading role to play in reaching out to their supporters and communicating the vital message that fans and supporters need to stay at home. I welcome that both clubs have agreed to reinforce that message.
"We still face a very real threat from the highly transmissible new variant and cannot risk people's health at this time, when we are at the very cusp of easing some restrictions."
It comes after Yousaf tweeted the game would be postponed if there was any police intelligence saying fans were about to "square off" against each other.
He said: "Our collective efforts are very much on ensuring the upcoming fixture between the two clubs is spoken about for events on the pitch, not off.
"We are pleased that the football clubs involved agreed to communicate robust messaging, stating unequivocally, that fans should stay at home.
"However, if police intelligence tells us, despite clear messaging, large groups of fans are going to gather and put public health at risk, we will need to very seriously consider taking action. Powers are open to us on that front.
"We are at the most critical juncture in our fight against the virus and we cannot, and simply will not, tolerate the shameful scenes we witnessed recently.”
Earlier on Friday, Celtic released a statement saying they had been clear about the need for fans to follow the rules throughout the pandemic - a message they would "re-emphasise" ahead of the game.
Rangers later confirmed the club took part in the meeting, adding: "This is to continue an open and constructive dialogue in relation to the upcoming Old Firm fixture at Parkhead. We are pleased that today's meeting was very constructive and we have agreed to support the 'stay at home' message.
"Rangers would like to reiterate manager Steven Gerrard's comments from last weekend, for supporters to stay at home and ensure the safety of themselves and others.”