* Brent crude prices climb back above $40
* U.S. stocks end higher, following oil
* Focus shifting to Thursday's ECB meeting (Updates with U.S. markets' closing levels)
By Caroline Valetkevitch
NEW YORK, March 9 (Reuters) - Oil prices resumed a more than month-long rally on Wednesday, helping to lift world stock markets, while the euro held steady ahead of this week's European Central Bank meeting.
Brent moved back above $40 a barrel on speculation the world's largest exporters would agree this month to freeze production and help reduce the largest global build in crude oil in years.
Brent rose $1.42 to settle at $41.07 a barrel, up more than 40 percent from its January lows, while U.S. crude increased $1.79 to settle at $38.29.
Wall Street stocks built on recent gains on Wednesday as the strong recovery in oil prices sent energy shares sharply higher. The S&P energy index rose 1.5 percent.
"Stability in that asset class (oil) for a period of time will allow for the correlation to break down," said Art Hogan, chief market strategist at Wunderlich Securities in New York.
The Dow Jones industrial average ended up 36.26 points, or 0.21 percent, to 17,000.36, the S&P 500 gained 10 points, or 0.51 percent, to 1,989.26 and the Nasdaq Composite added 25.55 points, or 0.55 percent, to 4,674.38.
MSCI's all-country world stock index gained 0.3 percent, while in Europe, the pan-regional FTSEurofirst 300 index closed 0.45 percent higher.
The biggest weekly draw in U.S. gasoline in almost two years persuaded traders that energy demand was improving despite crude stockpiles at record highs.
"Gasoline is the star of the show today," said Matt Smith, director of commodity research at New York-based energy data provider ClipperData. "Ongoing strength in demand has yielded a large draw to gasoline inventories despite a rebound in refinery runs."
Traders expect the ECB on Thursday to cut its deposit rate by at least 10 basis points and expand its asset-buying program. More ECB stimulus would put downward pressure on the euro but analysts have said ECB policymakers may not deliver the levels of easing traders expect.
The single currency was little changed at $1.1008, erasing an earlier 0.6 percent fall against the dollar. The dollar index, which measures the greenback against the euro, yen and four other currencies, dipped 0.1 percent.
In the bond market, yields of U.S. safe-haven government bonds rose as some investors bet the recent decline in yields due to global growth concerns was overdone.
Yields extended their climb as weak demand for $20 billion worth of 10-year government debt stoked a wave of selling.
The benchmark 10-year note was last down 17/32 in price to yield 1.891 percent, up from 1.834 percent late on Tuesday.
Copper, zinc and other base metals rose as speculators piled back into the market on hopes more production cuts would lead to shortages. Three-month copper in London closed up 1.4 percent at $4,935 a tonne. (Additional reporting by Tariro Mzezewa, Rodrigo Campos, Richard Leong and Barani Krishnan in New York; Editing by Nick Zieminski and Meredith Mazzilli)