TREASURIES-Europe worries, strong US auction boost govt bonds

* Strong three-year notes sale fuels further gains

* Worries over Europe, stocks drop revive safe-haven bid

* Long bonds up 2 points (Updates with closing prices)

By Burton Frierson

NEW YORK, Sept 7 (Reuters) - U.S. Treasuries rebounded on Tuesday after three straight losing sessions as weaker stocks, worries about Europe's financial sector and a strong three-year auction lifted debt prices.

Renewed worries that Europe's bank stress tests, aimed at shoring up financial sector confidence, were not particularly robust and that German banks may still have to raise a lot of capital hurt stocks and helped safe-haven debt. For details see[ID:nLDE6850Q9] and [.N].

Investors were also reassessing their initial relief about Friday's latest U.S. monthly jobs report, which was less grim than expected, while a well-received auction of $33 billion worth of three-year Treasuries boosted sentiment.

Coming off a three-day weekend following Monday's Labor Day holiday, the rally marked an abrupt turn after the bond market was pummeled last week on hopes that the U.S. economy was not in such a poor state as earlier thought.

"What's driving Treasuries today is just a lot of negative news out of Europe over the weekend and overnight," said Jason Rogan, director of U.S. Treasury trading at Guggenheim Capital Markets LLC.

"Stocks are down. It's been a slow grind up and then we pushed through a little bit after a decent three-year auction."

The 30-year bond US30YT=RR gained more than two points on the day, last trading up 2-6/32, yielding 3.66 percent versus Friday's close of 3.78 percent.

The benchmark 10-year note US10YT=RR was up almost a point, trading 28/32 higher in price, yielding 2.60 percent versus Friday's close of 2.70 percent.

FEARS AWAKENED

A report on the European banking system reawakened fears about the region's financial health. The Wall Street Journal report raised questions about bank stress tests carried out in the euro zone earlier in the year.

Separately, Germany's banking association said the country's 10 biggest banks may need 105 billion euros ($141 billion) of additional capital under a revamp of banking rules designed to prevent future financial crises. That news weighed on financial shares.

The gloom from Europe and the stock markets allowed bond traders to ignore some minor signs of weakness in an otherwise strong bond auction.

"With renewed European concerns and weaker risk assets today, the flight-to-quality bid to the Treasury market helped support today's three-year auction," said John Briggs, U.S. Treasury strategist at RBS Securities in Stamford, Connecticut.

The first of this week's three bond offerings totaling $67 billion, the three-year auction produced a record-low yield, the latest in a series for Treasury debt sales.

The sale attracted bids worth 3.21 times the amount on offer, right on their six-month average. The record-low yield at the auction also came in below expectations, indicating investors were willing to pay a small premium to get the bonds.

Among those negatives, primary dealers took 45.9 percent of the sale, above their six-month average of around 39 percent, meaning they were stuck with a larger-than-usual proportion of the offering to sell to the market.

That was the highest dealer take in percentage terms since May 2009, though auction sizes have been declining this year.

Foreign central bank and large institutional investor demand appeared soft compared with recent averages, based on the indirect bidder category, which accounted for about 42 percent of the sale.

This was well below the average of about 47 percent in the last six auctions, though higher than the two previous sales.

The recently growing direct bid accounted for 11.7 percent of the offering, below the six-month average of nearly 14 percent. (Additional reporting by John Parry; Editing by Dan Grebler)