(Updates all prices, adds inflation news, adds analyst quote)

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 bloc, was steady at 2.9587%. 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 rate hikes.

The two-year German bond yield - more sensitive

to ECB interest rate expectations - was unchanged at 2.559%.

Yields move inversely to prices.

Italian bond yields fell by more, with the 10-year yield

down 2.3 bps and the 2-year yield down 2

bps.

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 Iran 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 month-on-month.

The United States and Iran reached an agreement on Thursday

to extend their ceasefire and lift restrictions on shipping

through the Strait of Hormuz, sources told Reuters, though U.S.

President Donald Trump has yet to approve it and Iranian state

media said it had not been finalised.

Oil fell 1.8% to $92 a barrel.

"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," wrote Mohit Kumar,

chief European economist at Jefferies.

INFLATION JITTERS KEEP OPTIMISM IN CHECK

Kenneth Broux, head of corporate research for FX and rates

at Societe Generale, said euro zone bonds have been

underperforming U.S. recently.

"Europe as a whole is definitely underperforming the U.S.

after outperforming through May, I wonder how much of the lower

oil price and short-covering in Bunds is priced in. Support for

the 10-year Bund at 2.90% is a hurdle too far for now at least,"

he said.

With the Strait of Hormuz still largely closed and the

global flow of energy disrupted, fears of rising inflation in

the import-dependent euro zone had led traders to ramp up bets

on central bank rate hikes in recent weeks.

The worries subsided as optimism grew around a peace deal.

But key data reads are keeping inflation fears at the

forefront.

Friday's euro zone CPI figures come a day after figures

showed U.S. inflation increased at its fastest pace in three

years in April, cementing economists' views that the Federal

Reserve would hold interest rates unchanged well into ​next

year.

Also out on Friday was data showing France's economy shrank

slightly in the first quarter, missing the preliminary reading

of 0.0% for the euro zone's second-largest economy.

European Central Bank research showed on Friday that euro

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

their attitudes more quickly as a result of the upheaval of 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," said Rabobank analysts 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."

Money markets are betting on a 91% chance of a rate hike at

the ECB's next meeting on June 11.

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

they have to justify their inflation credibility. However, we do

not see a series of rate hikes and maintain our long position at

the front end of the curve," said Jefferies' Kumar.