GLOBAL MARKETS-Euro climbs on hope debt-crisis fix is near

* Euro rises on speculation euro zone will remain intact

* Bonds fall on profit-taking, hedge against debt solution

* Stocks falter, then fall on still gloomy economic data

* Oil slips on concerns about global slowdown and demand

By Herbert Lash

NEW YORK, June 4 (Reuters) - The euro rallied and bonds retreated from last week's record low yields on Monday as speculation increased that authorities will seek greater fiscal integration in the euro zone, among other actions to ease the region's festering debt crisis.

Stocks and oil prices fell, but the euro gained as investors speculated that new action may be in the works to address the debt crisis and keep Greece from leaving the euro zone.

German Chancellor Angela Merkel is pressing for much more ambitious measures, including a central authority to manage euro-area finances and major new powers for various European entities. In Spain, Prime Minister Mariano Rajoy is pushing for a direct European rescue of its troubled banks.

France and the European Commission signaled their support on Monday for an ambitious plan to use the euro zone's bailout fund as European officials try to reassure investors they can contain an escalating crisis.

Senior EU officials have promised firm decisions at a summit at the end of June to resolve the 2-1/2 year debt saga to deepen integration in the euro zone and underpin the common currency, showing they are committed to its future.

Still, there are divisions to be overcome.

Traders took profits in safe-haven U.S. and German debt, wary that a policy response to the euro zone's debt crisis might be in the works.

"It's relatively difficult to be positive on these developments," said Marius Daheim, senior fixed-income analyst at Bayerische Landesbank.

"But we haven't given up because the past has also taught us that European politicians usually move when things become really dangerous. I think we are quickly moving towards this point."

The benchmark 10-year U.S. Treasury note was down 12/32, with the yield at 1.497 percent.

The price of the 10-year German bond fell and its yield rose to 1.205 percent.

Another factor on traders' radar was that potential monetary easing may come from a meeting of the European Central Bank on Wednesday, as some investors positioned for an outside chance of a rate cut. Factory prices held steady in the euro zone in April, giving the ECB some room to cut rates.

"They (the ECB) have made it clear that they want the solution to come from Europe's leaders, but the recent deterioration in economic data and slide in asset prices makes easier monetary policy inevitable," said Kathy Lien, director of currency research at GFT in Jersey City, New Jersey.

The euro was 0.5 percent higher at $1.2490, off the lows last seen in July 2010 that it hit on Friday.

New orders for U.S. factory goods fell in April for the third time in four months as demand slipped, the latest worrisome sign for the economic recovery.

The Commerce Department said orders for manufactured goods dropped 0.6 percent, in contrast to economists' forecast calling for a 0.2 percent gain. The government also revised its estimate for new orders in March to show a steeper decline.

Stocks fell.

The Dow Jones industrial average fell 73.04 points, or 0.60 percent, to 12,045.53. The Standard & Poor's 500 Index shed 9.69 points, or 0.76 percent, to 1,268.35. The Nasdaq Composite Index dropped 16.65 points, or 0.61 percent, to 2,730.83.

In thin European markets, the FTSE Eurofirst 300 index of top shares provisionally closed down 0.5 percent at 949.94 points.

The MSCI world equity index slid 0.8 percent to 289.77 points.

Brent crude fell 61 cents to $97.82 a barrel.

U.S. crude slipped 6 cents to $83.16 a barrel.