(Updates prices at 1524 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 interest 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 8 basis points (bps) at

2.585%. The two-year yield, which is more sensitive

to changes in expectations for rates, was up 4 bps at 3.03%.

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 14 bps to 3.959%, which in turn pushed the

premium of Italian bonds over German up 6.7 bps to

135.9 bps.