  We study supersymmetric $AdS_3\times M^4$ solutions of $N=2$ gauged
supergravity in seven dimensions coupled to three vector multiplets with
$SO(4)\sim SO(3)\times SO(3)$ gauge group and $M^4$ being a four-manifold with
constant curvature. The gauged supergravity admits two supersymmetric $AdS_7$
critical points with $SO(4)$ and $SO(3)$ symmetries corresponding to $N=(1,0)$
superconformal field theories (SCFTs) in six dimensions. For
$M^4=\Sigma^2\times\Sigma^2$ with $\Sigma^2$ being a Riemann surface, we obtain
a large class of supersymmetric $AdS_3\times \Sigma^2\times \Sigma^2$ solutions
preserving four supercharges and $SO(2)\times SO(2)$ symmetry for one of the
$\Sigma^2$ being a hyperbolic space $H^2$, and the solutions are dual to
$N=(2,0)$ SCFTs in two dimensions. For a smaller symmetry $SO(2)$, only
$AdS_3\times H^2\times H^2$ solutions exist. Some of these are also solutions
of pure $N=2$ gauged supergravity with $SU(2)\sim SO(3)$ gauge group. We
numerically study domain walls interpolating between the two supersymmetric
$AdS_7$ vacua and these geometries. The solutions describe holographic RG flows
across dimensions from $N=(1,0)$ SCFTs in six dimensions to $N=(2,0)$
two-dimensional SCFTs in the IR. Similar solutions for $M^4$ being a Kahler
four-cycle with negative curvature are also given. In addition, unlike
$M^4=\Sigma^2\times \Sigma^2$ case, it is possible to twist by
$SO(3)_{\textrm{diag}}$ gauge fields resulting in two-dimensional $N=(1,0)$
SCFTs. Some of the solutions can be uplifted to eleven dimensions and provide a
new class of $AdS_3\times M^4\times S^4$ solutions in M-theory.
