June 4 (Reuters) - Euro zone government bond yields

dropped on Tuesday as weak economic data and falling oil prices

led investors to increase their bets on future European Central

Bank rate cuts.

Markets await U.S. jobs data later in the session after

economic figures showed on Monday that U.S. manufacturing

activity slowed for a second straight month in May, the latest

indications that a gradual economic slowdown is taking hold.

The number of people out of work in Germany rose more than

expected in May, data showed on Tuesday.

Oil prices eased as much as 1% in Asian trade, extending

losses from the previous session.

Germany's 10-year yield, the bloc's benchmark,

was down 5 basis points (bps) at 2.54%, after dropping 6.5 bps

the day before in its biggest daily fall since May 15.

"With just 35 bps discounted until year-end after this

week's prospective ECB rate cut and falling oil prices reviving

disinflation hopes, the momentum looks set to continue," said

Christoph Rieger, head of rates strategy at Commerzbank.

Investors are taking an ECB rate cut of 25 bps for granted

on Thursday but are uncertain about the outlook.

Money markets are pricing in 63 bps of ECB monetary easing

in 2024 - from less than 55 bps early on

Monday - which implies two rate cuts and slightly more than a

50% chance of a third move by year-end.

"Yet it seems markets are strongly driven by U.S. data when

deciding on the number of ECB cuts to expect this year," rate

strategists at ING said, after flagging that the correlation

between U.S. Treasury and Bund yields is increasing again.

The spread between U.S. and German 10-year yields

- a gauge of expectations for monetary policy

divergence between the U.S. Federal Reserve and the ECB - hit a

fresh 2-1/2-month low at 180.01 bps and was last at 183.8 bps, 3

bps wider from the day before.

The gap between French and German 10-year government bond

yields was still around 48 bps after Standard & Poor's cut its

rating on France's sovereign debt late Friday, a move that

market participants had widely expected.

Italy's 10-year yield fell 4 bps to 4.015% after

dropping 9 bps, its biggest daily drop since May 15.

"BTPs remain overall resilient though, defying more

fundamental headwinds as the manufacturing PMI kept falling,

taking the difference to Spain to a record high," Commerzbank's

Rieger added.

Manufacturing activity contracted in Italy at the steepest

pace this year, and grew at the fastest pace in more than two

years in Spain.

The yield gap between Italian and German bonds

, a gauge of the risk premium investors seek to

hold Italian bonds, was at 130 bps.

Germany's 2-year government bond yield, more

sensitive to policy rate expectations, was down 3 bps at 3.00%.