Glasgow and Peterhead, in Aberdeenshire, had the highest number of 20 minute-plus response times, followed by Edinburgh, Fraserburgh and Blairgowrie.
The Scottish Government response time target for such incidents is eight minutes.
But data obtained by the Scottish Liberal Democrats show the response time for "category A" incidents was more than 20 minutes on 2692 occasions in 2013/14.
The figure is slightly under 1.9% of the 142,340 category A call-outs the Scottish Ambulance Service received during the year.
Liberal Democrat MSP Jim Hume said the Government must provide ambulance staff with the support they need to improve response times. He said: "Our ambulance service does fantastic, life-saving work in communities around Scotland every day.
"But I think ambulance service staff would be among the first to recognise that these figures are hugely concerning.
"When lives are at stake we must do everything we can to reach those who need help as soon as possible.
"For people suffering from cardiac problems and other serious health conditions, every minute without treatment in an emergency can reduce the likelihood of survival. It is that simple.
"The eight-minute target for responses to serious incidents was introduced for good reason.
"Ministers now need to look closely at why this it is still being missed, and why so many patients have been forced to wait more than double this time to receive assistance."