* European shares steady after Asia rally, banks outperform
* Barclays surges 10 pct after it says seeking new funds
* Crude under $134 per barrel as Saudis mull production hike
* Dollar firm post-G8; Paulson says US favours strong dollar
By Mike Dolan
LONDON, June 16 (Reuters) - European shares were steady to firmer on Monday after strong rallies on Asia's bourses, with the banking sector outperforming during a critical week and Britain's Barclays <BARC.L> surging up to 10 percent.
The dollar was firm after the weekend meeting of Group of Eight finance ministers while oil prices eased on the prospect of an increase in ouput by Saudi Arabia.
Barclays' share gains came after the bank said it planned to sell stakes to outside investors and offer shares to existing shareholders to boost its balance sheet. Weekend press reports said it was close to securing almost $8 billion from sovereign wealth funds within the next two weeks.
The gains lifted banks across Europe in a important week for the sector which sees U.S. investment firms Goldman Sachs <GS.N> and Morgan Stanley <MS.N> report second-quarter earnings on Tuesday and Wednesday respectively. Commerzbank <CBKG.DE> rose 1.6 percent, Lloyds TSB <LLOY.L> 2.7 percent and BNP Paribas <BNPP.PA> gained 2 percent.
"The focus will be on the U.S. banks this week -- I expect Goldman to be solid and hope that all the bad news is out of the way on Lehman," said Heinz-Gerd Sonnenschein, strategist at Deutsche Postbank in Bonn.
The FTSEurofirst 300 <
> index of top European shares was little changed at 1,267.37 points, while Britain's FTSE 100 < > was up 0.2 percent.Energy stocks retreated in line with easier crude oil prices after United Nations chief Ban Ki-moon said at the weekend that Saudi Arabia was set to increase output to 9.7 million barrels per day next month.
London Brent crude <LCOc1> was down 86 cents to $134.25 a barrel and the stock prices of heavyweights BP <BP.L> and Royal Dutch Shell <RDSa.L> were off slightly.
Food producers Unilever <ULVR.L> and Cadbury <CBRY.L> fell between 2 and 3 percent after investment bank UBS downgraded the sector to a "sell" rating.
ASIA RALLY
Earlier, Asia stocks rallied as a U.S. dollar rebound boosted confidence in the region's exporters. The dollar was up 0.2 percent against the yen at 108.28 yen <JPY=>, although the euro recovered early losses to trade at $1.5417 <EUR=>.
Finance Ministers from the Group of Eight economic powers, meeting at the weekend, said little new on the outlook for the U.S. currency, although U.S. Treasury Secretary Henry Paulson reiterated his view that the U.S. government favoured a strong dollar as a matter of long-standing policy.
"A softer yen sparked hopes for upward earnings revisions for some exporters," said Takahiko Murai, general manager of equities at Nozomi Securities in Tokyo.
"But we have to brace for an eventual dramatic slowdown in Japan, where the stock market and the economy depend on overseas demand, considering the recent declines in Asian shares and rising inflation worries in emerging countries."
Japan's Nikkei share average <
> closed 2.7 percent higher with the yen near a four-month low against the dollar.South Korea's KOSPI <
> and Taiwan's TAIEX < > both rose 0.8 percent, led by the technology sector.The MSCI index of Asian equities <.MIAS00000PUS> rose 2 percent, the biggest gain in two months. Stocks in the Asia-Pacific region outside of Japan were up 1.3 percent on the day <.MIWD00000PUS>.
Equity markets in emerging Asia are viewed as particularly vulnerable to high oil prices because many of the region's central banks have had pro-growth stances for so long and their exchange rate policies are tightly woven to the U.S. dollar. For a FACTBOX, click on [
](Additional reporting by Kevin Plumberg in Hong Kong and Sitaraman Shankar in London; Editing by Gerrard Raven)