(Updates for afternoon session)

* Oil prices steady, slightly easing inflation concerns

* ECB expected to increase rates on June 11

By Sophie Kiderlin

LONDON, June 2 (Reuters) - Euro zone government bond

yields fell on Tuesday, partly reversing Monday's jump, as hopes

of a U.S.-Iran deal resurfaced despite lingering uncertainty.

U.S. President Donald Trump late on Monday said talks on ending

the conflict with Iran were continuing.

Iran is reviewing a potential agreement with the U.S. to

halt the war but has not communicated with Washington for a few

days, Iranian media reported on Tuesday.

Hopes of a deal tend to soothe bond markets as an agreement

could allow oil to again flow through the Strait of Hormuz,

lowering energy prices and reducing the need for central bank

rate hikes.

The yield on the German 10-year government bond, the euro

zone benchmark, fell 4 basis points to 2.97%, after rising 8 bps

on Monday. Yields move inversely to prices.

Germany's two-year yield, which is sensitive to rate

expectations, was last down 2 bps at 2.613%, after jumping more

than 9 bps on Monday.

Yields fell further earlier in the session but reversed some

of the fall that followed Iran's announcement of a halt in

communication with Washington.

Strong labour market data from the United States also pushed

shorter-dated bond yields in the U.S. and Europe higher.

Oil prices were steady, with Brent crude futures

last flat at $95.10 a barrel.

EURO ZONE INFLATION RISES

Markets also considered data that showed euro zone inflation

accelerated to 3.2% in May from 3% a month earlier.

It was driven by a 10.9% rise in energy costs and an

unexpectedly large increase in services inflation to 3.5% from

3%.

"For inflation in the eurozone, the only way is currently

up. Not a sharp up but a rather moderate and gradual lift,"

Carsten Brzeski, global head of macro at ING, said.

The European Central Bank meets to assess policy on June 11,

when Brzeski said the inflation increase could have determined a

rates rise.

"A week ahead of the next ECB meeting, this is the expected

uptick in inflation that will motivate the central bank to

decide on an 'insurance' hike," Brzeski said.

Money markets on Tuesday viewed a 25-bp rate hike next week

as almost certain, with a total of two such hikes expected this

year and a chance of a third.

Italy's 10-year yield fell 6 bps to 3.696%, also paring the

previous session's sharp rise.