Does Standard Model confirm that mass assigned by Higgs Mechanism creates gravitational field? I am not comparing passive gravitational mass with rest inertial mass. Is there an evidence in Standard Model which says that active gravitational mass is essentially mass assigned by Higgs mechanism.
 A: The mass of a particle is the energy that it has when it is at rest. The Higgs only makes it that particles oscillate between different helicities, so that you can make them be at rest, and their energy at rest is equal to the rate of oscillation between the two helicities. This energy gravitates like any other energy.
A: The standard model itself says nothing about gravity at all, so no.
In any case, the thing that couples to gravity is energy, not just mass. This is different from the mass that the Higgs field gives to particles, which is actually just (rest) mass, and does not count energy.
A: I will answer your deleted question, which is relevant. Read this link to get a framework of where the SM stands.
Look at table 1 and you will see that in the microcosm of quarks and leptons the gravitational interaction is so weak that it is completely irrelevant and certainly its effect on the values used of the standard model  cannot be measured with our present experimental accuracies.
You ask:

Is there an evidence in Standard Model which says that active gravitational mass is essentially mass assigned by Higgs mechanism.

The standard model  is mainly  descriptive, it is a method to mathematically tie together a very large number of experimental data, economically, for the three stronger forces, strong, electromagnetic and weak. Because the strength of the coupling  of the gravitational interaction is very much smaller than the coupling of these three forces ( Table 1 in link) there is no measurable predictable effect. In any case, as the quark and lepton masses are parameters in the SM, not predicted values,any tiny effect will be absorbed in the definitions.
The Stndard Model is not a theory of everything, but must be embedded in a theory of everything because it is really a shorthand for all the data we have up to now on quarks and leptons. A theory of everything will of course incorporate the gravitational force, and theorists are working on it, with prime candidate the string theories.
