  The experimental value for the isospin amplitude Re(A_2) in K->pi pi decays
has been successfully explained within the Standard Model, both within large N
approach to QCD and by QCD lattice calculations. On the other hand in both
approaches the theoretical values of Re(A_0) are by at least 30% below the data
so that the Delta I=1/2 rule in K->pi pi decays is not fully explained. While
this deficit could be the result of present theoretical uncertainties in both
approaches, it cannot be excluded that the missing piece in Re(A_0) comes from
New Physics. We demonstrate that this deficit can be significantly softened by
tree-level FCNC transitions mediated by a heavy colourless Z' gauge boson with
particularly chosen flavour violating couplings assuring negligible NP
contributions to Re(A_2) and significantly enhancing the contribution of the
leading QCD penguin operator Q_6 to Re(A_0). A large fraction of the missing
piece in the Delta I=1/2 rule can be explained in this manner for M_{Z'} in the
reach of the LHC, while satisfying constraints from epsilon_K,
epsilon'/epsilon, Delta M_K, LEP-II and the LHC. We identify quartic
correlation between Z' contributions to Re(A_0), epsilon'/epsilon, epsilon_K
and Delta M_K. We present correlations between epsilon'/epsilon and rare decays
K->pi nu bar{nu} with and without the Delta I=1/2 rule constraint and
generalize the whole analysis to Z' with colour (G') and Z with FCNC couplings.
In the latter case no improvement on Re(A_0) can be achieved without destroying
the agreement of the SM with the data on Re(A_2). Moreover, this scenario is
very tightly constrained by epsilon'/epsilon. On the other hand in the context
of the Delta I=1/2 rule G' is even more effective than Z': it provides the
missing piece in Re(A_0) for M_{G'}=(3.5-4.0) TeV.
