Energy is mass ($E=mc^2$) and energy is defined as force times distance. So what kind of force is associated with the energy making up the rest mass of a particle?
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Energy is the ability to do work. Work is force times displacement.
A particle with non-zero rest mass can be thought of having an inertial resistance to movement through space because of the Higgs interactions. These interactions translates to rest mass.
Moreover, in case of atoms there are strong force interactions that give up to 98% of total mass.
In general, the Einstein's equation simply tells that energy can behave like mass. In fact, mass and energy are two sides of the same coin.