(Updates throughout)

By Sophie Kiderlin

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

yields fell on Tuesday, partially reversing Monday's jump, as

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

uncertainty.

Optimism had faded heading into the week, but comments from U.S.

President Donald Trump late on Monday said talks on ending the

conflict with Iran were continuing.

On Tuesday, a source close to Iran's negotiating team told

Mehr News that Tehran has yet to respond to a proposed final

agreement with the U.S., and that internal discussions on the

text are ongoing.

Oil prices slipped, with Brent crude futures last

around 1.4% lower to $93.69 a barrel.

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

zone benchmark, fell 6.4 basis points to 2.9488%, after rising 8

bps on Monday.

Italy's 10-year yield dropped 8.8 bps to 3.6721%, also

paring the previous session's sharp rise.

INFLATION PICKS UP

Markets also considered fresh economic data, which showed

that euro zone inflation accelerated to 3.2% in May from 3% a

month earlier. This is above the European Central Bank's 2%

target, but was in line with a Reuters poll.

The increase was driven by a 10.9% rise in energy costs and

an unexpectedly large pickup in services inflation to 3.5% from

3.0%.

"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 data comes ahead of the European Central Bank's June 11

meeting, and was widely seen as bolstering the case for a rate

hike then.

"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 are pricing in about a 97% chance of a 25-bp rate

hike then, with a total of two such hikes seen this year and a

chance of a third.

Sandra Horsfield, economist at Investec, said: "the debate

will now shift to how many more hikes will have to follow at

subsequent meetings."

"Our baseline expectations is for one additional hike in

July. Whether that will be enough though will depend on the

evolution of the Iran conflict," she added.

Germany's two-year yield, sensitive to rate expectations, was

last down 4.1 bps at 2.5885%, after jumping more than 9 bps on

Monday.

Italy's two-year yield fell 6.4 bps to 2.7564%, also reversing

part of Monday's rise.