(Updates throughout; refreshes prices at 1150 GMT)

By Joice Alves and Amanda Cooper

LONDON, April 24 (Reuters) - Euro zone government bond

yields rose on Wednesday as markets digested data that showed

business activity has been a lot stronger than expected this

month, which might take some pressure off the European Central

Bank to cut rates beyond June.

The ECB has all but promised a rate cut in June, but its

policymakers are still debating what happens after that.

Bundesbank President Joachim Nagel, a key ECB policymaker,

on Wednesday said euro zone inflation could prove stubborn and a

rate cut in June might not necessarily be followed by more cuts.

"Such a step would not necessarily be followed by a

series of rate cuts," Nagel said in a speech in Berlin. "Given

the current uncertainty, we cannot pre-commit to a particular

rate path."

The yield on Germany's 10-year bond, the

benchmark for the euro zone, was up nearly 5 basis points (bps)

at 2.55%. The two-year yield, which is more sensitive

to changes in expectations for rates, was up 3 bps at 3.017%.

Ten-year yields have risen by 26 bps so far in April,

marking their largest one-month rise since September, while

two-year yields have risen 20 bps, reflecting more investor

appetite for shorter-dated debt as the first ECB rate cut nears.

"Nagel is downplaying the idea of back-to-back rate

cuts. A number of ECB Governing Council members have talked up

the idea of 3 or 4 rate cuts, with Wunsch suggesting maybe only

2 and Centeno suggesting more than 4 this year," Nomura

economist Andrzej Szczepaniak said, referring to remarks last

week by ECB policymakers

Mario Centeno

, who said even with two rate cuts, rates would still be in

restrictive territory, and

Pierre Wunsch

, who said multiple cuts were possible this year.

On Tuesday, a flash read of the

Purchasing Managers' Index (PMI) showed business activity in

the euro zone expanded at its fastest pace in nearly a year in

early April, as optimism remained strong and companies increased

headcount.

"The risk-on move has a bit more juice in our view and

thus 10-year Bund yields could see another uptick this week,"

ING strategists led by Padraig Garvey said in a note.

"The gradual recovery of the eurozone economy as

reflected by the PMIs is something that has been set in motion

for some time and shouldn't impact the European Central Bank's

decision to start cuts in June," they said.

Elsewhere in fixed income, yields on 10-year Italian

debt rose 7.3 bps to 3.889%, which in turn pushed

the premium of Italian bonds over German up 2.55

bps to 131.70 bps.

(Editing by Mark Potter, Peter Graff)