  Employing the covariant baryon chiral perturbation theory, we calculate the
leading and next-to-leading order two-pion exchange (TPE) contributions to $NN$
interaction up to order $O(p^3)$. We compare the so-obtained $NN$ phase shifts
with $2\leq L\leq 6$ and mixing angles with $2\leq J\leq6$ with those obtained
in the nonrelativistic baryon chiral perturbation theory, which allows us to
check the relativistic corrections to the medium-range part of $NN$
interactions. We show that the contributions of relativistic TPE are more
moderate than those of the nonrelativistic TPE. The relativistic corrections
play an important role in F-waves especially the $^3\text{F}_2$ partial wave.
Moreover, the relativistic results seem to converge faster than the
nonrelativistic results in almost all the partial waves studied in the present
work, consistent with the studies performed in the one-baryon sector.
