GLOBAL MARKETS-German bund yields gain, lift euro; stocks edge down

* Oil prices rise (Updates to U.S. early afternoon trading)

By Caroline Valetkevitch

NEW YORK, May 12 (Reuters) - German bond yields climbed on Tuesday on optimism that inflation may have bottomed in the euro zone, generating demand for European currencies, while volatility in global bond markets weighed on stock indexes.

U.S. 10-year Treasury yields eased from six-month highs as some buyers came back to the market ahead of the government's sale of $24 billion in new three-year notes.

U.S. stocks were flat, with bond market volatility adding to investor anxiety over the perilous state of Greece's finances.

German bond yields have surged in recent weeks, boosted by optimism that inflation may have bottomed in the euro region, according to some analysts. The move has been exacerbated by investors unwilling to enter the market until the sell-off shows signs of stabilizing.

The U.S. dollar slumped against the euro and Swiss franc.

Benchmark 10-year Treasuries were last up 9/32 in price to yield 2.24 percent, after earlier hitting 2.37 percent.

"We saw some real money buying off the lows this morning," said Sean Murphy, a Treasuries trader at Societe Generale in New York.

The Treasury is due to sell $24 billion in three-year notes on Tuesday, $24 billion in 10-year notes on Wednesday and $16 billion in 30-year bonds on Thursday. Corporate and other supply is also coming to market.

Elevated U.S. yields mean higher corporate borrowing costs, which could hit shares across the world.

German 10-year yields were last up at 0.69 percent.

Less than a month ago, German 10-year yields hit a record low of 0.05 percent, driven down by a 1-trillion-euro European Central Bank bond-purchase scheme intended to boost inflation.

MSCI's all-country world index of stock performance in 46 countries was down 0.2 percent.

The Dow Jones industrial average was down 10.28 points, or 0.06 percent, at 18,094.89. The Standard & Poor's 500 Index was down 3.27 points, or 0.16 percent, at 2,102.06. The Nasdaq Composite Index was down 4.98 points, or 0.10 percent, at 4,988.60.

In deal news, AOL shares jumped after Verizon Communications said it would buy the company in a $4.4 billion deal.

GREEK CONCERNS

In the forex market, the euro was last up 0.7 percent against the dollar at $1.12310 and was set for its first session of gains in four against the greenback.

Investors have been concerned that debt-burdened Greece could run out of cash.

Euro zone finance ministers, who met on Monday, acknowledged progress in talks between Greece and its creditors but said more work was needed to close a cash-for-reforms deal. Athens stocks , however, rose 0.2 percent.

Oil prices, up more than 50 percent from their January lows, rose further as dollar weakness trumped concerns about oversupply. Brent crude was up $1.80 at $66.71 a barrel. U.S. crude was up $1.34 at $60.59.

Gold rose as much as 1 percent as the dollar declined. Spot gold touched a session high of $1,196.60 an ounce. (Additional reporting by Karen Brettell in New York and Nigel Stephenson in London; Editing by Mark Trevelyan, Meredith Mazzilli and Dan Grebler)