The Scottish Sports Council is making pound;2.1 million available from the Lottery Sports Fund over three years and is currently consulting on an extension of the programme. BT is lending support.
Stewart Harris, director of Team Sport Scotland, told a meeting in Glasgow last week there was widespread support for programme beyond the 12 councils which took part in the piloting.
The programmes are designed to foster activity among young children and introduce them to core skills. Evidence from England shows increased confidence among primary teachers in delivering PE and higher skill levels among pupils.
Mr Harris said: "A fundamental feature, however, is that local authorities must give their support. We will be asking serious questions of their commitment to PE and sport for young people."
There is enough money in the pot to provide every primary with equipment and training.
In England, where the programme is established, school inspectors reported growing evidence of improved skills. Steve Grainger, managing director of the Youth Sports Trust, said there was an increased profile for PE among pupils and parents.
Scottish councils can apply to implement the scheme in some or all primaries. Independent schools that can demonstrate community links or sports development openings will also be eligible.