(Updates prices moves, adds Ireland bank liability guarantee)
* Stocks fall but meltdown fears abate
* U.S. futures point to higher Wall Street open
* Dollar gains against yen, euro
By Jeremy Gaunt, European Investment Correspondent
LONDON, Sept 30 (Reuters) - World stocks fell to near three-year lows on Tuesday but fears of a major meltdown following historic Wall Street losses eased as European losses were muted.
The U.S. Congress's rejection of a bank rescue package tore nearly 9 percent off the broad S&P 500 <.SPX> on Monday but European shares and many Asian stock markets clawed back early losses on hopes the U.S. plan would eventually go through.
U.S. stock index futures also pointed to a higher opening, suggesting some belief that Monday's selloff was over done.
"It's certainly my working assumption that there (will be) some sort of agreement reached in the U.S. and based on that I would expect the market to recover quite strongly from yesterday's sell-off," said Darren Winder, equity strategist at Cazenove.
Angst over the battered financial sector continued, nonetheless, with Belgian-French financial services group Dexia <DEXI.BR> getting a 6.4 billion euro ($9.18 billion) capital boost from public shareholders to help it fight the global credit crisis.
Ireland also offered to guarantee all bank deposits for two years to improve banks' access to funds on international markets. It also guarantees covered bonds, senior debt and dated subordinated debt.
European stocks fell as much as 2 percent in early trading and Japan's Nikkei closed 4.12 percent lower after the deep losses on Wall Street in the wake of Congress's failure to agree a $700 billion plan to buy up toxic debt from the financial industry.
Globally, MSCI's main world stock index <.MIWD00000PUS>, a benchmark for many leading investors, was down 0.8 percent, adding to a 6.84 percent loss on Monday that saw the index's market capitalisation plunge $1.73 trillion.
The FTSEurofirst 300 index of top European shares <
> recovered to be flat, however, having fallen 5.2 percent on Monday.Earlier, the Nikkei average hit a three-year closing low, shedding 483.75 points to 11,259.86, the lowest finish since June 2005. It earlier lost nearly 5 percent.
Other Asian stocks recovered, however. Hong Kong's Hang Seng index <
> closed 0.8 percent higher, while South Korea's KOSPI < > pared losses to end down 0.6 percent. Both had fallen more than 5 percent early in the day.
SEEKING SAFETY
The dollar rebounded against the yen and euro, helped in part by banks scrambling to raise dollar funds because money markets remained frozen.
"The risk aversion story is getting worse and the dollar will likely be supported, especially against the euro and sterling," said Ian Stannard, senior foreign exchange strategist at BNP Paribas.
The dollar was up 0.9 percent at 104.98 yen <JPY=> after hitting an overnight low of 103.50 yen. The euro was down 0.3 percent at $1.4377 <EUR=> after hitting an overnight low of $1.4338.
Euro zone government bonds were mixed.
Oil <CLc1> was trading close to $96.50 a barrel after slumping almost 10 percent in the previous session. (Editing by Mike Peacock)