* Euro falls as ECB pledges inflation fight
* European shares rally; global markets slip on jobless claims
* U.S. bond prices rise, Friday's labor report in focus
* Brent creeps up from 5-month low under $105
(Adds opening of U.S. markets, byline, dateline previously LONDON)
NEW YORK, April 3 (Reuters) - Global equity markets traded slightly lower on Thursday as a larger-than-expected rise in U.S. jobless claims kept investors on edge a day ahead of the government's monthly labor market report, while the dollar rose against the euro after the European Central Bank pledged action if needed to battle low inflation.
Initial claims for unemployment benefits increased 16,000 to a seasonally adjusted 326,000 in the week ended March 29, the U.S. Labor Department said. Economists had forecast a rise to 317,000 new claims.
Separately, the Institute for Supply Management said its services sector index rose to 53.1 in March, slightly below expectations though comfortably ahead of February.
Stocks on Wall Street traded edged lower, but shares in Europe were higher. A measure of global equities, MSCI's all-country world stock index fell 0.2 percent.
"The information we've gotten so far today is a little bit on the light side with respect to leading us towards bullishness, but not enough to make us run screaming 'sell' down the halls," said Kim Forrest, senior equity research analyst, Fort Pitt Capital Group in Pittsburgh
The Dow Jones industrial average fell 17.59 points or 0.11 percent, to 16,555.41, the S&P 500 lost 2.43 points or 0.13 percent, to 1,888.47 and the Nasdaq Composite dropped 16.545 points or 0.39 percent, to 4,259.91.
European shares rallied, with a number of national indexes hitting multi-year highs, after the ECB president, Mario Draghi, opened the door for unconventional measures to thwart the risk of deflation in the euro zone.
The FTSE Eurofirst 300 index of leading European shares was up 0.13 percent at 1,345.11 points.
Euro zone banks were among the biggest gainers, with Natixis up 4.1 percent, UniCredit up 2.8 percent and Banco Espirito Santo up 2.7 percent
The euro dropped after the ECB said it was ready to deploy anything in its monetary policy toolbox if inflation stays too low for too long even as it kept interest rates steady.
The currency, shared by 18 nations, dipped as low as $1.3699 before paring some losses to trade 0.37 percent lower at $1.3715.
Euro zone annual inflation ticked down to 0.5 percent in March, its lowest level since the region's economy was deep in recession in 2009 and its sixth month in what Draghi has described as "the danger zone" below 1 percent.
"The ECB is being slightly more dovish than the market expected," said Kathy Lien, managing director at BK Asset Management in New York. "The main takeaway is that the council is considering unusual techniques, and that's negative for euro/dollar."
Longer-dated U.S. Treasuries yields edged lower on the jobless claims report, causing some jitters ahead of the monthly nonfarm payrolls report due Friday.
The benchmark 10-year U.S. Treasury note rose 4/32 in price to yield 2.7862 percent.
Brent crude rose slightly to nearly $105 a barrel but remained near five-month lows as expectations of a deal to reopen vital Libyan oil ports were balanced by doubts that a lasting resolution was imminent.
Brent crude rose 37 cents to $105.16 a barrel. U.S. crude, or West Texas Intermediate (WTI), fell 5 cents to $99.57 a barrel.
(Reporting by Herbert Lash; Additional reporting by Jamie McGeever in London; Editing by Leslie Adler)