  We present a novel ten-dimensional description of ambitwistor strings. This
formulation is based on a set of supertwistor variables involving pure spinors
and a set of constraints previously introduced in the context of the $D=10$
superparticle following a ten-dimensional twistor-like construction introduced
by Berkovits. We perform a detailed quantum-mechanical analysis of the
constraint algebra, we show that the corresponding central charges vanish, and
after considering a convenient gauge fixing procedure, physical states are
found. Vertex operators are explicitly constructed and, by noticing a relation
with the standard pure spinor formalism, scattering amplitudes are shown to
correctly describe $D=10$ super-Yang-Mills interactions. As in other
ambitwistor string models, amplitudes are found to be localized on the support
of the scattering equations, and thus this work provides a bridge between
Berkovits' construction and the Cachazo-He-Yuan formulae. After extending the
pure spinor twistor transform to include an additional supersymmetry, our
results are immediately generalized to Type IIB supergravity.
