* Italian 10-year debt yield hits 4.5-year high of 3.783 percent
* Euro rallies after falling to 10-day low
* World stock index posts fourth straight week of losses
* Oil up but posts weekly loss on stock build, trade tensions (Updates after U.S. market close)
By Rodrigo Campos
NEW YORK, Oct 19 (Reuters) - Stocks dipped on Friday, dragging a global index into a fourth consecutive weekly loss, while the euro and sterling rallied against the dollar after a report said Britain is ready to drop a key Brexit demand.
Oil prices rose on signs of surging demand in China, although prices fell for a second week running as U.S. inventories swelled.
Strong earnings boosted shares early on Wall Street but concerns over economic growth in China and Europe lingered, dragging indexes lower in afternoon trade.
"There a lot of cross-currents right now, with Italy, housing weakness, interest rates (rising) ...," said Michael Antonelli, managing director of institutional sales trading at Robert W. Baird in Milwaukee.
The pan-European STOXX 600 index lost 0.12 percent and MSCI's gauge of stocks across the globe shed 0.08 percent.
The Dow Jones Industrial Average rose 64.89 points, or 0.26 percent, to 25,444.34, the S&P 500 lost 1 point, or 0.04 percent, to 2,767.78 and the Nasdaq Composite dropped 36.11 points, or 0.48 percent, to 7,449.03.
Emerging market stocks were flat. MSCI's broadest index of Asia-Pacific shares outside Japan closed 0.13 percent higher.
In currencies, the British pound and the euro rose after Bloomberg News reported that British Prime Minister Theresa May is ready to drop a key Brexit demand in order to make a deal for Britain to leave the European Union.
Earlier, EU negotiator Michel Barnier said a Brexit deal was 90 percent done although hurdles remained.
Sterling was last trading at $1.3068, up 0.39 percent on the day. The euro rose 0.56 percent to $1.1516.
The dollar index fell 0.26 percent.
The Mexican peso touched a five-week low versus the greenback after ratings agency Fitch revised Pemex's credit rating outlook to negative citing uncertainty over the Mexican national oil company's future business strategy.
Mexico's currency lost 0.62 percent versus the U.S. dollar at 19.26. It earlier touched 19.34 per dollar, the weakest in five weeks.
The Japanese yen weakened 0.28 percent versus the greenback at 112.50 per dollar.
Italian assets were sold heavily earlier in the session a day after the European Union called Rome's draft budget an "unprecedented" breach of EU fiscal rules. The selling subsided after European Economics Commissioner Pierre Moscovici said he wanted to reduce budget tensions with Italy.
The closely watched Italian/German bond yield spread touched a 5-1/2-year high of 338.4 basis points before tightening to 306.8.
Italy's benchmark 10-year bond yield rose as high as 3.783 percent, the highest since February 2014. It last traded at 3.569 percent.
Oil prices rose on signs of surging demand in China, but the market remained concerned over rising U.S. inventories and trade wars that could curb economic activity.
U.S. crude rose 0.95 percent to $69.30 per barrel and Brent was last at $79.94, up 0.82 percent on the day.
The benchmark U.S. Treasury yield traded within the previous session's range. The U.S 10-year note last fell 4/32 in price to yield 3.1902 percent, from 3.175 percent late on Thursday.
Reporting by Rodrigo Campos, Stephanie Kelly, April Joyner Karen Brettell and Richard Leong in New York; additional reporting by Christopher Johnson in London; Editing by Nick Zieminski and James Dalgleish