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 LCOc1 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.