GLOBAL MARKETS-Shares ease on Greek exit fears; dollar gains

* China's rate cut initially lifts stocks

* Oil weakens on signs of renewed shale production (Adds U.S. market open, byline, dateline; previous LONDON)

By Herbert Lash

NEW YORK, May 11 (Reuters) - Global equity markets eased on Monday after a cut in Chinese interest rates initially kept shares near record highs, but a lack in progress in resolving Greece's financial woes weighed on stocks and weakened the euro against the dollar.

Gains by mining stocks helped to support some European equities after the rate cut in China, the world's biggest consumer of copper and other metals.

But signs that U.S. shale oil production was recovering sent oil prices lower and made energy the biggest losing sector on the benchmark S&P 500.

A strong jobs report on Friday that showed the U.S. economy was picking up steam and helped boost Wall Street by more than 1 percent was old news by Monday, with investors again looking at the potential implications of a Greek exit from the euro zone.

"The market's focus was distracted away from Greece last week with the U.K. elections and with the (U.S.) payroll data. The second that was out of the way, (investors) jumped on it," said Richard Scalone, co-head of foreign exchange at TJM Brokerage in Chicago.

Greek bond yields edged up as euro zone finance ministers met in Brussels to discuss a cash-for-reforms deal with Athens, which faces the first in a series of large debt repayments this week.

MSCI's all-country world index of stock performance in 46 countries fell 0.03 percent, while key UK, German and French national stock indexes were lower. The pan-European FTSEurofirst 300 index rose 0.38 percent to 1,596.79 points, lifted by financial stocks.

On Wall Street, the Dow Jones industrial average fell 35.16 points, or 0.19 percent, to 18,155.95. The S&P 500 slid 3.76 points, or 0.18 percent, to 2,112.34 and the Nasdaq Composite lost 3.43 points, or 0.07 percent, to 5,000.12.

The U.S. dollar rose against the euro on renewed worries over a Greek exit from the euro zone.

The euro fell 0.35 percent to $1.1164, while the dollar rose 0.15 percent to 94.944 against a basket of six currencies. Against the yen, the greenback gained 0.13 percent to 119.94.

U.S. Treasury yields rose, dragged higher by a continued selloff in German government bunds and as investors readied for the U.S. government to sell $64 billion in new debt this week.

Benchmark 10-year Treasuries were last down 17/32 in price to yield 2.2109 percent. German 10-year note yields rose 8 basis points to 0.598 percent.

Oil slipped towards $65 a barrel on signs that U.S. shale oil production was recovering after a recent price rally renewed concerns of a growing global supply glut.

Brent crude for June was down 64 cents at $64.75 a barrel. U.S. light crude for June delivery fell 25 cents to $59.14 a barrel. (Reporting by Herbert Lash)