  In an earlier paper [arXiv:1408.0484] gauge invariant and background
covariant equations for closed string modes were obtained from the exact
renormalization group equation of the world sheet theory. The background metric
(but not the physical metric) had to be flat and hence the method was not
manifestly background independent. In this paper the restrictions on the
background metric are relaxed. A simple prescription for the map from loop
variables to space time fields is given whereby for arbitrary backgrounds the
equations are generally covariant and gauge invariant. Extra terms involving
couplings of the curvature tensor to (derivatives of) the Stueckelberg fields
have to be added. The background metric is chosen to be the physical metric
without any restrictions. This method thus gives manifestly background
independent gauge invariant and general covariant equations of motion for both
open and closed string modes.
