  We study inverse $\pi$-extensions of the semigroup $\mathbb{Z}_+$. It is
shown that $\pi$-extension of the semigroup $\mathbb{Z}_+$ is inverse, iff its
$\pi$-extension coincides with $\pi(\mathbb{Z}_+)$. The existence of a
non-inverse $\pi$-extension for semigroup $\mathbb{Z}_+$ is proved.
