* Euro zone bourses fall on Greece, driving bond yields up
* China's rate cut initially lifts stocks
* Oil weakens on signs of renewed shale production (Adds close of European bond, stock market)
By Herbert Lash
NEW YORK, May 11 (Reuters) - Global equity markets eased on Monday on a dip in energy shares and fears a resolution to Greece's financial woes is not in sight, leading the euro to weaken against the dollar.
A cut in Chinese interest rates initially lent support to Asian and some European shares, especially miners, as China is 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 sector that weighed the most on the S&P 500. U.S. oil drillers added rigs to the Permian Basin for the first time this year, industry data showed last week.
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, as investors again eyed the potential implications of a Greek exit from the euro zone.
Greece paid about 750 million euros to the International Monetary Fund a day before it was due, two Greek finance ministry officials told Reuters, but it was not enough to stop worries over future payments.
"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 0.15 percent, and key UK, German and French national stock indexes were lower. The pan-European FTSEurofirst 300 index rose 0.31 percent to 1,596.79 points, lifted by financial stocks.
On Wall Street, the Dow Jones industrial average fell 46.14 points, or 0.25 percent, to 18,144.97. The S&P 500 slid 4.66 points, or 0.22 percent, to 2,111.44 and the Nasdaq Composite added 4.42 points, or 0.09 percent, to 5,007.97.
The U.S. dollar rose against the euro on renewed worries over a Greek exit from the euro zone.
The euro fell 0.46 percent to $1.1152, while the dollar rose 0.24 percent to 95.024 against a basket of six currencies. Against the yen, the greenback gained 0.2 percent to 120.03.
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 21/32 in price to yield 2.2253 percent. German 10-year note yields rose to 0.605 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 47 cents at $64.92 a barrel. U.S. light crude for June delivery fell 26 cents to $59.13 a barrel. (Reporting by Herbert Lash; Editing by Nick Zieminski)