* MSCI world share index hits six-month high
* Europe climbs, led by FTSE
* Oil hits highest since Nov, Brent nears $70 a barrel (Updates with close of European markets)
By Chuck Mikolajczak
NEW YORK, April 2 (Reuters) - World stock markets were little changed on Tuesday after touching a six-month high as investors took a breather following a three-day run of gains while oil prices continued to climb amid the increased possibility of tightening supply.
MSCI's key gauge of global equities had rallied 1.1% on Monday, its best performance in three weeks, as manufacturing data in China and the United States put recession worries at bay. On Tuesday, the index held close to the unchanged mark for most of the session.
Major U.S. indexes were little changed, although the blue-chip Dow Jones Industrial Average was dragged down by a slump of 12.58% in Walgreens Boots Alliance Inc after the drugstore chain cut its 2019 profit growth forecast. Economic data did little to stunt growth worries.
New orders for key U.S.-made capital goods slipped in February and shipments were unchanged, but data for January was revised slightly higher, which could support views that the manufacturing sector was stabilizing in the wake of the data on Monday.
"We've gotten to a place and time where we are going to need new evidence to move this market higher," said Art Hogan, chief market strategist at National Securities in New York.
"Incrementally better-than-expected data might move this market higher, which was not the case in today's durable goods number."
The Dow Jones Industrial Average fell 105.98 points, or 0.4%, to 26,152.44, the S&P 500 lost 1.96 points, or 0.07%, to 2,865.23 and the Nasdaq Composite added 12.16 points, or 0.16%, to 7,841.07.
After a sluggish start, European shares built some late momentum to close at their highest level in six months, helped by gains in insurers and automakers.
Europe was led by a jump of 1% in London's FTSE 100 index as sterling weakened. That came as the European Union said Britain could be heading for a potentially disorderly exit in 10 days as Prime Minister Theresa May met with ministers to work out ways to break the Brexit deadlock.
But sterling reversed course following the close of European indexes, after May said Britain needed a further extension to ensure it leaves the European Union with a deal in a timely manner.
The pan-European STOXX 600 index rose 0.35%.
The dollar index rose 0.16%, with the euro down 0.15% to $1.1195. Sterling was last trading at $1.3106, up 0.05% on the day.
The Brexit concerns also pushed yields on U.S. Treasuries lower from one-week highs as investors looking for bargains and a safe-haven bid stepped in.
Benchmark 10-year notes last rose 5/32 in price to yield 2.4813%, from 2.497% late on Monday.
Oil prices continued to rally, with crude prices hitting their highest levels of the year and Brent moving closer to the $70 a barrel mark for the first time since mid-November. The gains came on the prospect of more sanctions against Iran and further Venezuelan disruptions that could deepen an OPEC-led supply cut.
U.S. crude rose 1.33% to $62.41 per barrel and Brent was last at $69.20, up 0.28% on the day.
Additional reporting by Sruthi Shankar in Bengaluru; Editing by Bernadette Baum and Lisa Shumaker