  We show that a recently proposed framework that provides a simple connection
between Majorana neutrinos and an invisible axion in minimal scalar extensions
of the standard electroweak model can be naturally embedded in a classically
scale-invariant setup. The explicit breaking of the scale invariance \`a la
Coleman-Weinberg generates the Peccei-Quinn and electroweak scales. The
spontaneous breaking of the chiral $U(1)_{PQ}$ triggers the generation of
neutrino masses via Type-II seesaw and, at the same time, provides a dynamical
solution to the strong CP problem as well as the axion as a dark matter
candidate. The electroweak and neutrino mass scales are obtained via a
technically natural ultraweak limit of the singlet scalar interactions.
Accordingly, a realistic and perturbatively stable scalar spectrum, possibly in
the reach of the LHC, is naturally obtained. A very light pseudodilaton
characterizes such a setting. The vacuum stability of the extended setup is
discussed.
