  A metric space $X$ is {\em injective} if every non-expanding map $f:B\to X$
defined on a subspace $B$ of a metric space $A$ can be extended to a
non-expanding map $\bar f:A\to X$. We prove that a metric space $X$ is a
Lipschitz image of an injective metric space if and only if $X$ is Lipschitz
connected in the sense that for every points $x,y\in X$, there exists a
Lipschitz map $f:[0,1]\to X$ such that $f(0)=x$ and $f(1)=y$. In this case the
metric space $X$ carries a well-defined intrinsic metric. A metric space $X$ is
a Lipschitz image of a compact injective metric space if and only if $X$ is
compact, Lipschitz connected and its intrinsic metric is totally bounded. A
metric space $X$ is a Lipschitz image of a separable injective metric space if
and only if $X$ is a Lipschitz image of the Urysohn universal metric space if
and only if $X$ is analytic, Lipschitz connected and its intrinsic metric is
separable.
