(Updates headline, prices at 1420 GMT)

By Alun John and Joice Alves

LONDON, April 30 (Reuters) - Euro zone government bond

yields rose on Tuesday as inflation in the bloc steadied in

March and the economy rebounded in the first quarter, while

separate data showed U.S. labour costs increased more than

expected in the first quarter.

While the U.S. data could remove some pressure on the

Federal Reserve to cut rates, the euro zone figures have not

disrupted market bets on a European Central Bank rate cut in

June - but left the future path open.

The Employment Cost Index (ECI), the broadest U.S. measure

of labour costs, increased 1.2% last quarter. Economists polled

by Reuters had forecast the ECI would advance 1.0%.

In the euro zone, inflation steadied at 2.4% in April,

Tuesday flash data showed. An important indicator of underlying

price pressures slowed, but services inflation was 3.7%, a

decline but possibly still too high for comfort.

Meanwhile, gross domestic product in the 20-country bloc

increased by an above-expectation 0.3% quarter-on-quarter.

The German 10-year bond yield, the benchmark for

the euro zone bloc, was up nearly 5 basis points at 2.57%.

It hit a five-month high of 2.65% last Thursday, but has

since been falling, helped somewhat by initial inflation data

from Germany and Spain on Monday.

"The key point from the data is the ECB can cut in June -

the bar not to is very high - the question is do they then cut

in July," said Andrzej Szczepaniak, senior European economist at

Nomura.

Government bonds remain highly sensitive to changes in

expectations for central bank interest rates. Market pricing

currently indicates a roughly 70% chance of a 25-basis-point ECB

cut in June, and two or three cuts in total this year.

Investors will also be watching the Federal Reserve, which

begins its two-day meeting on Tuesday - no rate change is

expected but chair Jerome Powell's Wednesday post-meeting press

conference will be watched closely given sticky U.S. inflation

and strong growth.

"The new narrative is what happens if we see what we're now

seeing in the U.S. in the euro zone in a few months' time.

Growth is expected to pick up and should services inflationary

pressure remain sticky for longer, that causes problems for the

ECB even if they begin cutting in June," said Szczepaniak.

Italy's 10-year yield was higher by 4.4 bps​ at

3.86%, and the gap between Italian and German bunds

widened 2 bp to 128.8 bps.

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

sensitive to European Central Bank rate expectations, was up 6.6

bps at 3.02%.