State and municipal government fiscal conditions that have been battered by the economic downturn will get some relief as growth picks up, but a full recovery will be slow in coming, Federal Reserve Chairman Ben Bernanke said on Wednesday.

If the economy continues to strengthen at about the pace projected by the Federal Reserve and many private forecasters, states and localities may start to get a little breathing space, he said in remarks prepared for delivery to a conference.

However, because the pace of recovery will be modest given the depth of the downturn, it will be some time before state and local fiscal conditions return to normal, he added.

Municipal bond markets seem to be functioning reasonably well now that states and localities are addressing budget shortfalls, he said. Measures of risk in municipal bond markets, while high, have looked somewhat better recently, he said.

(Reporting by Kristina Cooke, writing by Mark Felsenthal; Editing by Leslie Adler)