* Bank shares drive world stocks to 3-month low after Brexit vote
* Wall Street set to follow Europe and Asia lower
* Sterling drops more than 3 percent to fresh 31-year low
* Safe havens in demand; Japan raises yen intervention rhetoric
* Bond yields drop, Spain outperforms after Sunday election
By Nigel Stephenson
LONDON, June 27 (Reuters) - European bank shares and sterling were on track for their biggest two-day slides on record on Monday as the fallout of Britain's shock vote to quit the European Union sowed turmoil in global financial markets for a second day.
U.S. index futures were down 0.7 percent ESc1 1YMc1 , indicating Wall Street would follow European markets down.
Investors sought safe havens such as the yen, gold and low-risk government debt. Moves were not as extreme as on Friday when stocks fell by their most in almost five years but the combined falls on Friday and Monday broke records in some assets.
British finance minister George Osborne sought to reassure markets, saying the world's fifth-largest economy was strong enough to cope with the Brexit-inspired volatility, but the positive impact on sterling was only fleeting.
"This Brexit decision has taken the markets by total surprise. I would remain on the sidelines - no reason to step in yet," said Hampstead Capital hedge fund manager Lex Van Dam.
Markets bet on a further cut in Bank of England interest rates, almost fully pricing in a 25 basis point cut by the end of the year in another blow to sterling and to banks already facing reduced earnings as a result of Britain leaving the EU.
An index of European bank shares .SX7P fell 7.5 percent, taking the decline in the last two trading days to around 20 percent, equating to a loss of 168 billion euros in market capitalisation. Royal Bank of Scotland shares RBS.L fell 23 percent while Barclays BARC.L shed 18 percent.
Italian banks also suffered. UniCredit CRDI.MI fell 7.7 percent. The government was looking at options to help its banks and prevent further share price falls. pan-European FTSEurofirst 300 stocks index .FTEU3 , which fell 7 percent on Friday in its biggest plunge in nearly eight years, lost a further 2.9 percent on Monday, for its biggest two-day fall since the aftermath of the Lehman collapse in 2008.
Britain's FTSE 100 index .FTSE ebbed a further 2.1 percent on Monday and Germany's DAX .GDAXI lost 2.2 percent.
Spain's IBEX index .IBEX initially rose after acting prime minister Mariano Rajoy's People's Party fared better than expected in weekend elections but the gains melted away and the index was last down 1.4 percent.
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World stocks measured by MSCI .MIWD00000PUS hit their lowest level since March, down 0.9 percent. The index's fall since the Brexit vote was its biggest since last August when sharp falls in Chinese shares slammed work markets.
Sterling fell nearly 4 percent to $1.3152, surpassing its Friday low as yields on 10-year British government debt fell below 1 percent for the first time GB10YT=RJR .
It fell 2.5 percent to 83.33 pence against the euro EURGBP= and 3.9 percent to about 134 yen GBPJPY= .
"Uncertainty equals currency weakness, we know this, and there is no sense that this (sterling) is a value trade right now and that you have to get back in. It is too early for anyone to start calling a bottom," said Neil Mellor, a currency strategist at Bank of New York Mellon (NYSE:BK) in London.
The euro EUR= , also seen vulnerable to the exit from the EU of its second-largest economy, fell 1.3 percent to as low as $1.0969. The yen firmed to as high as 101.37 per dollar JPY= .
Government officials stepped up warnings that they could intervene in currency market to stabilise the yen, whose strength harms exporters.
This helped Japan's Nikkei 225 .N225 share index, which closed 2.4 percent higher. MSCI's broadest index of Asia-Pacific shares outside Japan .MIAPJ0000PUS fell 0.4 percent. Companies with UK exposure in particular came under pressure.
Yields on core government debt fell again. German 10-year bond yields DE10YT=TWEB , the benchmark for euro zone borrowing costs, fell as low as minus 0.11 percent but held above Friday's record low of almost minus 0.17 percent.
OUTPERFORM
Spanish 10-year bonds ES10YT=TWEB outperformed those of other lower-rated southern euro zone countries. Their yields were down 18 bps at 1.46 percent after Sunday's election.
U.S. Treasury yields also fell. The 10-year note US10YT=RR fell more than 10 bps to as low as 1.46 percent, still above Friday's low of 1.41 percent.
Gold XAU= , which saw its biggest rise since 2009 on Friday, stood at $1,329 an ounce, up 1.1 percent on the day.
Brent crude oil LCOc1 was higher in Asian trade on a view that Brexit would have minimal impact on global oil demand. But, by midday in London, it was down 18 cents at $48.23 a barrel. (Aditional reporting by Hideyuki Sano in Tokyo, Nichola Saminather in Singapore, Patrick Graham, Alistair Smout and Dhara Ranasinghe in London; Editing by Toby Chopra)