* Oil adds to 2 pct rally, stretching beyond $51 a barrel
* Economic optimism aided by Japan data; flu risk worsens (Updates prices, adds world stocks at 4-month peak)
By Jonathan Leff
SINGAPORE, April 30 (Reuters) - Oil rose well above $51 a barrel on Thursday, extending the previous day's gains as traders focused on improving economic data and draining fuel stocks rather than the worsening swine flu outbreak.
A surprise 4.7 million barrel decline in U.S. gasoline stocks ahead of the driving season and stock market gains aided oil's 2 percent rise on Wednesday, although prices remained stuck in the $45-$55 range that has bound them for the past six weeks.
U.S. light, sweet crude <CLc1> for June delivery rose 56 cents to $51.53 a barrel by 0524 GMT. Brent crude <LCOc1> gained 41 cents to $51.19.
Prices are on track to gain 3 percent this month, their third monthly rise, but the rebound from February's $33 low has stalled as traders await further evidence that the economy's decline is easing, offering an improved outlook for oil demand.
"I think there's going to be a bit more of tracking broadly sideways as the market tries to interpret the signals from the economic data and whether we're at the trough in the economic cycle," said Ben Westmore, commodities analyst at National Australia Bank.
And while Wednesday's U.S. government data showed a surprise decline in nationwide gasoline inventories that eliminated a supply surplus heading into peak driving season, he noted that crude stocks continue to bulge. [
]The Energy Information Administration weekly report showed a 4.1 million barrel increase in crude oil stockpiles, bringing inventories to a new 19-year high, and a 1.8 million barrel increase in unseasonally high distillate stocks.
News that the World Health Organization had raised its threat level on the swine flu virus also failed to dampen the mood as traders took a wait-and-see approach over whether it would become a pandemic that could further cut fuel demand. [
]"The market is waiting for a bit more clarification about how bad a problem it is," said Westmore.
ECON HOPES GROW
World stocks struck a four-month peak on Thursday, powered by gains in Asia, as investors took heart from signs of improvement in the U.S. economy suggesting regional exporters may need to start cranking up production. [
]Traders looked past the surprisingly big 6.1 percent contraction in the economy in the first quarter to focus on the details of a big run-down in inventories.
Hints of future expansion were further reinforced by comments from the U.S. Federal Reserve, which said the pace of deterioration in the economy appeared to be slowing. [
] [ ]Adding to the growing glimmers of economic hope, industrial output in hard-hit Japan rose 1.6 percent in March, the first gain in six months, contributing to a 4 percent gain in the Nikkei average <
>. [ ]A Reuters' poll forecast world oil demand would fall this year by 1.56 million barrels per day, much more than previously expected, as growth stalls in emerging powerhouses such as China and consumption declines in the developed world. [
] (Additional reporting by Maryelle Demongeot; Editing by Michael Urquhart)