  The paramagnetic spin-triplet superconductor UTe$_2$ has attracted
significant attention because of its exotic superconducting properties
including an extremely high upper critical field and possible chiral
superconducting states. Recently, ultraclean single crystals of UTe$_2$ have
become available, and thus measurements on these crystals are crucial to
elucidate the intrinsic superconducting properties. Here, we report the
thermodynamic critical field $H_{\rm c}$, the lower critical field $H_{\rm
c1}$, and the upper critical field $H_{\rm c2}$ at low fields of these
high-quality single crystals. From the comparison of the anisotropies in
$H_{\rm c1}$ and $H_{\rm c2}$, we find that the experimental $H_{\rm c1}$
values with the magnetic field along $b$- and $c$-axes are anomalously
enhanced, showing unusual low-temperature upturns. We propose an effect of the
strong Ising-like ferromagnetic fluctuations on the vortex line energy as the
origin of the anisotropic enhancement of $H_{\rm c1}$.
