  It was shown in arXiv:1410.7168 that compactifying $D=6$, $\mathcal{N}=(1,0)$
ungauged supergravity coupled to a single tensor multiplet on S$^3$ one gets a
particular $D=3$, $\mathcal{N}=4$ gauged supergravity which is a consistent
reduction. We construct two supersymmetric black string solutions in this
3-dimensional model with one and two active scalars respectively. Uplifting the
first, one gets a dyonic string solution in $D=6$ that has been known for a
long time. Whereas, uplifting the second solution, one finds a very interesting
configuration where magnetic strings are located uniformly on a circle in a
plane within the 4-dimensional flat transverse space and electric strings are
distributed homogeneously inside this circle. Both solutions have
$\mathrm{AdS}_3 \times$ S$^3$ limits.
