* U.S. money market showing more encouraging signs

* No dealer bids at Fed auction suggests less strain

* U.S. commercial paper market supply rebounds in week

* Three-month dollar Libor falls a 10th straight session (Updates market action, changes byline, dateline, previous LONDON)

By Richard Leong

NEW YORK, April 9 (Reuters) - The U.S. money market showed some improvement on Thursday, as dealers chose not to borrow securities from the U.S. Federal Reserve to raise cash and data showed a rebound in commercial paper activity.

Across the Atlantic, banks lowered what they charge each other for dollars, euros and sterling in the London Interbank Offered Rate (Libor) market, reflecting greater risk appetite tied to optimism for a recovery in the banking sector and U.S. consumer spending.

This upbeat outlook sparked a rally on Wall Street and in other risky assets like corporate bonds.

"They are all positive signs. We hope to see more of them going forward, but we need to see a lot more of them," said Ward McCarthy, managing director at Stone & McCarthy Research Associates in Princeton, New Jersey.