  We work out the consistent AdS$_3\times S^3$ truncations of the bosonic
sectors of both the six-dimensional ${\cal N}=(1,1)$ and ${\cal N}=(2,0)$
supergravity theories. They result in inequivalent three-dimensional
half-maximal ${\rm SO}(4)$ gauged supergravities describing 32 propagating
bosonic degrees of freedom apart from the non-propagating supergravity
multiplet. We present the full non-linear Kaluza-Klein reduction formulas and
illustrate them by explicitly uplifting a number of AdS$_3$ vacua.
