EURO GOVT-Economic worries send yields to new lows

* Safe-haven rates, yields mark new lows as stocks slide * Global recovery worries underpin government bond markets

* 10, 30-yr yields on track for historic monthly falls

* Bund option expiries at 135.0 eyed

(Adds index extensions, updates to mid-session)

By Kirsten Donovan

LONDON, Aug 31 (Reuters) - Safe-haven German Bund yields and 10-year interest swap rates hit record lows on Tuesday after Asian stocks slid overnight and European shares fell on worries about the faltering U.S economic recovery.

Tokyo stocks fell over 3.5 percent on Tuesday, their worst daily drop in three months, as disappointment after the BOJ expanded its fund supply tool in a bid to halt the rise of the yen JPY= -- widely seen as an ineffective move-- also weighed.

European shares .FTEU3 were almost one percent lower and on track to end down on the month.

"It's the same global recovery story, or lack thereof," said Credit Agricole rate strategist Orlando Green.

"The market very much seems to be looking to the downside in terms of yield and the 10-year Bund could drift towards the round number of two percent."

Five- and 10-year German bond yields fell to 1.183 percent and 2.084 percent respectively, while Bund futures FGBLc1 marked new highs at 134.77.

"We've gone up a long way on very little news. It's self- fulfilling in that every time we make a new high there's going to be another round of stops," said a trader.

Ten-year yields DE10YT=TWEB, down over 55 basis points in August, were on track for their biggest monthly fall since December 2008, while 30-year yields, down over 70 basis points EU30YT=RR, are on track for their biggest monthly fall since the introduction of the euro in 1999.

Although Bund futures retreated slightly -- they were last 34 ticks higher at 134.53 -- traders said option expiries could see the contract take another run higher later in the session.

Bund future call options at 135.0 have the largest open interest by a sizeable margin, a trader said.

Also in play were month-end index extensions although much of the move was likely to have taken place already. Barclays calculated euro zone month-end index duration extension at 0.03 years, in line with the average for August, which is typically relatively low given a lack of redemptions and issuance.

The 10-year German interest swap rate EURAB6E10Y= fell to 2.28 percent and at the shorter end Euribor interest rate futures <0#FEI=> with expiries through 2012 hit record highs.

"Rates strips and the like are pricing fast towards low rates forever rather than just for low rates for longer," Nomura rate strategists said.

At 1020 GMT, two-year bond yields DE2YT=TWEB were almost a basis point higher at 0.604 percent, with 10-year yields DE10YT=TWEB down nearly 3 bps at 2.105 percent .

"The policy backdrop for government bonds is set to remain constructive as we see no scope for exit strategies or rate hikes in the US, UK or euro zone into next year," said Lena Komileva, head of G7 economics at Tullett Prebon.

Strengthening market expectations that the ECB will keep its main interest rate unchanged at an historic low of 1.0 percent well into 2011, data showed euro zone inflation slowed as expected in August and unemployment was flat for the fifth month running in July as rising employment in powerhouse Germany was offset by fewer jobs in Belgium, Spain and Ireland [ID:nLDE67U0IQ].

Peripheral yield spreads and credit default swap prices were broadly steady.

Further clues on the health of the U.S. economy will come from snapshots of business activity in New York City and the Chicago area and consumer confidence readings from the Conference Board.

(Reporting by Kirsten Donovan; Editing by Ron Askew)