  We study the problem of two interacting particles in a one-dimensional
quasiperiodic lattice of the Harper model. We show that a short or long range
interaction between particles leads to emergence of delocalized pairs in the
non-interacting localized phase. The properties of these Freed by Interaction
Kinetic States (FIKS) are analyzed numerically including the advanced Arnoldi
method. We find that the number of sites populated by FIKS pairs grows
algebraically with the system size with the maximal exponent $b=1$, up to a
largest lattice size $N=10946$ reached in our numerical simulations, thus
corresponding to a complete delocalization of pairs. For delocalized FIKS pairs
the spectral properties of such quasiperiodic operators represent a deep
mathematical problem. We argue that FIKS pairs can be detected in the framework
of recent cold atom experiments [M.~Schreiber {\it et al.} Science {\bf 349},
842 (2015)] by a simple setup modification. We also discuss possible
implications of FIKS pairs for electron transport in the regime of
charge-density wave and high $T_c$ superconductivity.
