Members of the Scottish Obesity Alliance have written to the First Minister urging her to include plans for these regulations as part of her legislative programme to be announced next month.
The letter calls for restrictions on multi-buy deals on food and drinks high in fat, sugar and salt, warning obesity in Scotland is facing a "major public health crisis".
The alliance highlights almost a third of adults (29%) in Scotland are obese, as are 13% of children, according to figures from a Scottish Government report last October.
Its letter states: "We are bombarded by promotions on food and drink products that contain excessive amounts of calories, fat, sugar and salt.
"Restriction is needed across all types of promotions on high fat, sugar and salt products but regulation to restrict multi-buy price promotions should be prioritised as a first step in a multi-stage approach."
The letter warns failing to take urgent action will "undermine" the Scottish Government's target to tackle health inequalities and reduce childhood obesity by 50% by 2030.
A total of 20 organisations including health charities, medical royal colleges, campaign groups and professional bodies have co-signed the letter.
Alliance chairwoman Elma Murray said "The Scottish Obesity Alliance have identified securing restrictions on multi-buy price promotions as one of the first actions that can be taken by the
Scottish Government to work towards an ambition to reduce levels of overweight and obesity.
"It is therefore important that the new Programme for Government contains a commitment to make this a reality."
Cancer Research UK is one of the organisations which endorsed the letter and its public affairs manager Gordon Matheson said the Scottish Government needs to act now.
He said: "Carrying too much weight is the most common cause of avoidable cancer in Scotland after smoking and is a major public health crisis."
Professor Steve Turner, Officer for Scotland for the Royal College of Paediatrics and Child Health warned "bold" restrictions are needed.
He said: "More than 28% of children in Scotland are overweight or obese.
"Research tells us that the food and drink children see strongly influences the food choices they make and how much they eat."
The Royal College of Physicians of Edinburgh called for nutritional food to be promoted alongside restrictions of multi-buy promotions on junk food.
A four-month Scottish Government public consultation on restricting junk food promotions closed in January.
A Scottish Government spokesman said: "Tackling obesity is a public health priority and our Diet and Healthy Weight Delivery Plan includes a wide range of bold measures designed to help families make healthier choices.
"One key component is ending our nation's damaging relationship with junk food that is high in fat, sugar or salt, and reducing associated health harms.
"One of the ways we are seeking to do this is by restricting the promotion and marketing of some of discretionary foods high in fat, sugar or salt with little or no nutritional benefit.
"We have consulted on the steps to achieve this and our analysis will be published in the near future."