GLOBAL MARKETS-Greece hopes lift European shares; dollar, Treasury yields climb

* Greece optimism lifts shares

* Wall Street stocks end slightly higher

* U.S. dollar gains as Fed seen raising rates this year (Updates with U.S. market closing levels)

By Caroline Valetkevitch

NEW YORK, June 23 (Reuters) - Optimism that a deal could still be at hand to stave off a Greek default lifted European shares and kept a floor under U.S. stocks on Tuesday, while the U.S. dollar and bond yields climbed as prospects improved for a Federal Reserve interest rate hike this year.

A seven-year high in new U.S. single-family home sales last month, combined with other data, helped bolster the case for lifting benchmark U.S. interest rates.

Fed Governor Jerome Powell said the U.S. economy could be ready for a first rate hike in September followed by a second increase in December and that the economy is likely to strengthen in the second half of the year.

Overseas, Greece presented new proposals on Monday that euro zone leaders welcomed as a basis for a possible agreement to unlock aid and avert default and a potential exit from the euro. But some euro zone leaders cautioned that much work still needed to be done, and some Greek lawmakers reacted angrily to concessions offered by Athens.

"The market seems to expect that this will end favorably, or at least benignly, but I think people need to be nimble right now as circumstances could change at any time," said Steve Sosnick, equity-risk manager at Timber Hill/Interactive Brokers (NasdaqGS: IBKR - news) Group in Greenwich, Connecticut.

The U.S. dollar index was up 1.1 percent, while the euro fell to a two-week low of $1.11350, down nearly 2 percent, before recovering to $1.11740, off 1.47 percent on the EBS trading platform.

MSCI (NYSE: MSCI - news) 's all-country stock index was up 0.03 percent.

On Wall Street, the Dow Jones industrial average rose 24.29 points, or 0.13 percent, to 18,144.07, while the S&P 500 gained 1.35 points, or 0.06 percent, to 2,124.2.

The Nasdaq Composite added 6.12 points, or 0.12 percent, to 5,160.10, another record close.

The pan-European FTSEurofirst 300 index ended up 1.1 percent, while Greek stocks jumped 6.1 percent.

Also fueling the rally in Europe were better-than-expected data on factory and service sector activity in France, Germany and the euro zone overall.

In the bond market, benchmark 10-year U.S. Treasury notes were last down 12/32 in price to yield 2.41 percent, from a yield of 2.36 percent late Monday.

Crude futures rallied about 2 percent, with oil products rebounding ahead of U.S. inventory data expected to show strong demand for gasoline.

Brent crude futures rose $1.11 to settle at $64.45 a barrel, while U.S. crude settled at $61.01, up 63 cents.

Gold eased as the euro slid against the dollar and as stock markets gained. Spot gold was down 0.7 percent at $1,176.79 an ounce. (Additional reporting by Ryan Vlastelica and Barani Krishnan in New York, and Nigel Stephenson in London; Editing by Nick Zieminski and Meredith Mazzilli)