(Updates at 1015 GMT)

By Harry Robertson

LONDON, June 3 (Reuters) - Euro zone bond yields fell

slightly on Monday after data showed the bloc's factory activity

remained weak in May, but the moves were muted as traders

awaited a likely European Central Bank rate cut on Thursday.

Germany's 10-year bond yield, the benchmark for

the euro zone bloc, fell 2 basis points (bps) to 2.626%.

Final readings of survey-based gauges of Europe's

manufacturing sector showed activity remained below the mark

denoting growth for a 23rd month.

The purchasing managers' index surveys also came in slightly

lower than preliminary readings, although the downturn was still

moderated compared to April.

"Overall, these data suggest that conditions in

manufacturing remained difficult midway through Q2," said Claus

Vistesen, chief euro zone economist at Pantheon Macroeconomics.

"But they also clearly signal that the recession...is now

easing."

Italy's 10-year yield was down 4 bps at 3.92%,

and the gap between Italian and German yields

narrowed to 129 bps.

The market's focus this week is on the ECB's interest

rate decision on Thursday, when it is all but certain to cut

rates to 3.75%, from the current record high of 4%.

Investors will be looking out for any hints about when

the next reduction might come, with some on the ECB's Governing

Council pushing back against the idea of a July cut. Data last

week showed that euro zone inflation was stronger than expected

in May.

Germany's two-year bond yield, which is more

sensitive to European Central Bank rate expectations, was down 1

bp at 3.069%.

"While there is a consensus on this first rate cut, the

pace of future cuts is already subject to lively debate within

the Council," said Franck Dixmier, global chief investment

officer for fixed income at Allianz Global Investors, in emailed

comments.

"Future inflation data is likely to be volatile, and the

ECB is likely to caution that it is sticking to its gradual

approach to cutting rates."

French bonds showed little notable reaction to ratings

agency S&P downgrading the country's credit rating late on

Friday.

Just before the EU's parliamentary elections, S&P cut

France's rating to "AA-" from "AA", saying higher than expected

deficits would push up debt in the euro zone's second-biggest

economy.

France's 10-year bond yield was down 3 bps

at 3.108%, broadly in line with the move in other euro zone

country bonds.

The spread between U.S. 10-year Treasury and German bund

yields held steady at 185 bps.