* Investors price in three ECB rate hikes as oil prices

surge

* ECB's Joachim Nagel warns rates may rise if inflation

expectations de-anchor

* German, Italian, French bond yields climb; U.S. and UK

yields also rise

(Updates with U.S. inflation data, refreshes prices)

By Sophie Kiderlin

LONDON, May 12 (Reuters) - Euro zone bonds sold off for

a fourth day on Tuesday, as hopes faded for a peace deal in the

Iran war, which pushed up the oil price again and prompted

investors to price in three rate hikes by the European Central

Bank this year.

U.S. President Donald Trump said the ceasefire with Iran was

"on life support" after Tehran rejected a U.S. proposal to end

the conflict and stuck to a list of demands that Trump has

described as "garbage".

"Clearly there has been a lot of back and forth gyrations

that we've had over the last few weeks when it seemed there was

no hope, then there was a lot of hope, then we're back to little

hope. So it's very hard to know what the final endpoint is,"

Sandra Horsfield, economist at Investec, said.

Germany's 2-year yield, which is regarded as more

sensitive to rate expectations, was 6.4 basis points higher at

2.709%, up for a fourth day in a row as prices fell.

Interest rate expectations picked up again on Tuesday, with

money markets pricing in around three 25-basis-point rate hikes

from the ECB by the end of the year. The probability of a policy

increase in June was last close to 90%.

ECB policymaker Joachim Nagel said on Tuesday the ECB must

raise interest rates if the oil shock resulting from the Iran

war threatens to unmoor inflation expectations in the euro zone.

"Should the effects prove large or persistent, and

especially if they threaten to de-anchor long-term inflation

expectations, our mandate requires us to act," Nagel, the head

of Germany's Bundesbank, told a central bank event.

Andrzej Szczepaniak, senior European economist at Nomura,

said it was almost guaranteed that inflation expectations would

rise further, opening the door for the ECB to raise rates at its

June meeting.

The central bank will try to get ahead of so-called

second-round inflation effects like a wage-price spiral, he

said.

"Basically, the ECB will be saying by raising rates once or

twice, hey, look, we're not going to leave inflation or

inflation expectations unchecked. We're going to make sure we

get ahead of things and ensure that inflation stabilizes at

target over the medium term," Szczepaniak said.

BOND YIELDS SURGE ACROSS EURO ZONE

The yield on the German 10-year bond, the benchmark

for the euro zone, was 5.9 bps higher at 3.103%. Italy's 10-year

bond yield jumped nearly 10 bps to 3.881% and French

10-year bond yields rose 8 bps to 3.742%.

The German federal statistics office on Tuesday said that

EU-harmonised inflation stood at 2.9% in April, confirming

preliminary figures.

U.S. data showed consumer prices rose at a brisk pace for a

second month in a row in April, as the war with Iran pushed up

energy costs and food prices surged. U.S. Treasury yields rose

4.5 bps to 4.457%.

Meanwhile, UK gilts were battered by political turmoil in

Britain, where Prime Minister Keir Starmer vowed to stay in his

job, defying mounting pressure within his own party. Thirty-year

gilt yields hit their highest since 1998 at one

point on Tuesday and were last 10 bps higher on the day at

5.77%.

(Additional reporting by Amanda Cooper, Editing by John Mair,

Andrew Heavens and Ros Russell)