[tex4ht] \autoref from hyperref with tex4ht

[Martin Heller]

I've posted this on comp.text.tex too, but as tex4ht comes up rarely in 
that newsgroup I thought I might have better chances of a reply here.

Is it possible to get the same output from \autoref using htlatex as 
when using pdflatex?

Minimal example demonstrating the difference:

\documentclass{article}
\usepackage{hyperref}

\begin{document}

\begin{figure}
  \caption{My figure.}
  \label{fig}
\end{figure}

See~\autoref{fig}.

\end{document}

When compiled with pdflatex I get "See Figure 1".

When compiled with htlatex I get "See 1".

Can \autoref be configured to give "See Figure 1" in both cases? I tried 
\providecommand\figureautorefname{Figure} but it doesn't do the trick.