Can $E=mc²$ be treated as violation to law of conservation of mass? I mean should it be more correct to tell" total energy and mass of the universe" is conserved than" total mass of universe is conserved"?
A remarkable and most popular achievement of SR (special relativity) theory is the equivalence of mass and energy. The famous equation should be read in the rest frame of the particle where m is its rest mass. The rest mass is the particle's internal energy.
The law of conservation of mass was stated in the pre-relativistic physics. With SR it was overridden by the law of conservation of energy.
The equation simply states that bodies with mass contain energy, even when at rest in free space. Having said this, you could still interpret the equation as the union of two conservation laws, mass conservation and energy conservation, and in this this case you would be saying that the relation between mass and energy requieres that both together must be conserved, rather that each one individually.