  We develop a new off-shell formulation for six-dimensional conformal
supergravity obtained by gauging the 6D ${\cal N} = (1, 0)$ superconformal
algebra in superspace. This formulation is employed to construct two invariants
for 6D ${\cal N} = (1, 0)$ conformal supergravity, which contain $C^3$ and
$C\Box C$ terms at the component level. Using a conformal supercurrent
analysis, we prove that these exhaust all such invariants in minimal conformal
supergravity. Finally, we show how to construct the supersymmetric $F \Box F$
invariant in curved superspace.
