(Updates with afternoon trading)

* Inflation data mixed in major euro zone economies

* ECB seen likely to hike interest rates in June, but

markets doubt further tightening this year

* Iran deal hopes, oil prices driving rate expectations

By Lucy Raitano

LONDON, May 29 (Reuters) - Euro zone bond yields

steadied on Friday as investors assessed mixed inflation figures

from the bloc's major economies while awaiting more details of a

potential deal to reopen the Strait of Hormuz and extend the

U.S.-Iran ceasefire.

Germany's 10-year bond yield, the benchmark for the

euro zone, was steady at 2.96%. It has fallen 7 basis points

this month, as investors grew more optimistic about a potential

Iran peace deal, in turn bringing oil prices down and tempering

bets on European Central Bank interest rate hikes.

The two-year German bond yield - more sensitive to

ECB interest rate expectations - was a whisker higher at 2.56%.

Yields move inversely to prices.

Inflation in the euro zone's four largest economies hovered

above the ECB's 2% target for a third straight month in May,

preliminary data showed on Friday, as a rise in fuel costs

triggered by the war began to feed through to other prices.

Country-specific figures were mixed. While German figures were

cooler than expected, the Spanish reading was hotter than

expected, as was Italy's. In France, inflation came in below the

forecast but crept higher on a month-over-month basis.

That data did little to change expectations of an ECB rate hike

next month, which money markets see as all but certain. However,

they have turned more sceptical about policy tightening later in

the year, pricing a second hike by October, but only seeing a

small chance of a third move by the end of the year.

CHANGING ATTITUDES AMONG EURO ZONE CONSUMERS

Rate expectations are swinging on headlines from the Gulf and

resulting moves in oil prices.

Iran said on Friday it was looking for actions, not words

from the U.S. after Reuters reported, citing sources, that

President Donald Trump was weighing an initial agreement to

extend the ceasefire and open the strait.

"In terms of market reactions, if a deal is agreed upon, we

should see another leg higher in risky assets and lower in

rates. However, positioning suggests that the rates market

should see a greater reaction than equities," Mohit Kumar, chief

European economist at Jefferies, wrote in a note.

"For the ECB, we can see one hike (in June), simply because they

have to justify their inflation credibility," Kumar said.

Underscoring that idea, ECB research on Friday showed euro

zone consumers, already scarred by the Ukraine war, have changed

their attitudes more quicklyin response to the Iran conflict,

meaning the economic hit could be deeper and faster.

"Today's inflation data are further cementing the case for a

rate hike," Rabobank analysts said in a note, as they also

flagged a pick-up in consumers' medium-term inflation

expectations.

"However, we still believe that the current backdrop is less

conducive to broader and protracted inflationary pressures than

2021-2022."

Separate data, however, showed France's economy shrank

slightly in the first quarter, missing the preliminary reading

of no change in the euro zone's second-largest economy.