* U.S. nonfarm payrolls fall 345,000 in May, below forecast

* Drop smallest since September, fuels recovery optimism

* Six million U.S. jobs lost since recession started

* Jobless rate hits 9.4 pct, highest in almost 26 years (Adds consumer credit, closing market prices)

By Lucia Mutikani

WASHINGTON, June 5 (Reuters) - The pace of U.S. job losses slowed sharply last month, the strongest sign to date that the recession is diminishing, even as the unemployment rate hit its highest in nearly 26 years.

The Labor Department said on Friday that U.S. employers cut 345,000 jobs in May, the fewest since September and far less than economists had forecast. They cut 504,000 jobs in April.

However, the unemployment rate raced to 9.4 percent, the highest since July 1983, from 8.9 percent in April, partly because people who had given up looking for work reentered the labor market, a sign economic confidence was returning.

"It keeps hopes alive for a full recovery in the U.S. economy by the second half. It's a step in the right direction," said John Canally, investment strategist and economist for LPL Financial in Boston.