(Updates at 1507 GMT)

By Harry Robertson

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

Monday after data showed factory activity remained weak in the

bloc and shrunk in the U.S. in May, as markets awaited a likely

European Central Bank rate cut on Thursday.

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

the euro zone bloc, fell 7 basis points (bps) to 2.577%.

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."

U.S. manufacturing activity also slowed for a second

straight month, the Institute for Supply Management's PMI survey

showed, further supporting the idea that U.S. growth is set to

slow as previous rate hikes bite.

"Overall, the data is consistent with the view that the

manufacturing sector is not going to add meaningfully to

economic activity this year," said ING chief international

economist James Knightley.

European bonds have often been driven by expectations for

Federal Reserve policy over the last two years, given the size

and importance of the U.S. economy.

Markets were not fully pricing the first quarter-point rate

cut from the Fed until November, with around a two-in-three

chance they move in September.

Italy's 10-year yield was down 7.5 bps at

3.887%, and the gap between Italian and German yields

stood at 130 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 5

bps at 3.033%.

"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 7 bps at

3.0668%, broadly in line with the move in other euro zone

country bonds.