By Hilary Russ

NEW YORK (Reuters) - European and U.S. shares rebounded on Tuesday and the battered pound rose as markets digested Britain's vote last week to leave the European Union.

Bargain-hunting lifted stocks worldwide for the first time in three days, but there was still widespread uncertainty as the bloc's leaders, including soon-to-be-ex UK Prime Minister David Cameron, held their first post-vote meeting in Brussels.

Britain's finance minister, George Osborne, said the country would have to cut spending and raise taxes to stabilize the economy after a third credit ratings agency downgraded its debt.

"The lingering uncertainty favors further downside in the coming months as we have seen with other shocks of the past 5 years," said Jeffrey Kleintop, chief global investment strategist at Charles Schwab & Co., Inc.

Still, the stock sell-off paused on Tuesday. European shares <.FTEU3> rose 2.4 percent, clawing back some of their 10 percent loss the wake of the UK's vote.

Bank shares recovered and led markets higher. The S&P financial index <.SPSY> rose 2.47 percent.

Britain's Lloyds <LLOY.L> and Barclays <BARC.L> gained through the day, jumping 7.43 percent and 3.38 percent respectively. Italy's UniCredit <CRDI.MI> rose but then pulled back, last up 1.52 percent, and Spain's Bankia <BKIA.MC> surged more than 9 percent before falling back slightly to a 8.24 percent gain.

On Wall Street, the Dow Jones industrial average <.DJI> rose 269.48 points, or 1.57 percent, to 17,409.72, the S&P 500 <.SPX> gained 35.55 points, or 1.78 percent, to 2,036.09 and the Nasdaq Composite <.IXIC> added 97.42 points, or 2.12 percent, to 4,691.87.

Sterling also got a reprieve, recovering early though stalling in late trading in London.

The pound rebounded by as much as 1.5 percent <GBP=D4> from its 11 percent plunge after the British referendum. But that paled compared with the currency's decline to a 31-year low on Friday.

Sterling gained 0.86 percent against the greenback at $1.334 <GBP=D4> and rose 2.32 percent to 137.02 against the yen <GBPJPY=>.

U.S. Treasury yields opened higher but then flattened as worries about sluggish economic growth played off the rebound in stocks.

"A lot of the drop in yields will be sustained even as fears of the Brexit outcome fades. There's simply not enough growth," said Robert Tipp, chief investment strategist at Prudential Fixed Income in Newark, New Jersey.

Treasury prices, which more inversely to yields, added to gains after Moody's Investors Service changed its outlook on 12 UK banks and building societies late on Tuesday.

Benchmark 10-year notes <US10YT=RR> were little changed in price to yield 1.461 percent. The 10-year yield hit a near four-year low of 1.406 percent on Friday, Reuters data showed.

The 30-year bond <US30YT=RR> was up 4/32 in price to yield 2.274 percent, down 0.6 basis point from late on Monday.

Gold stepped back after two heady days. Spot gold <XAU=> was down 1 percent at $1,311.60 an ounce at 3:15 p.m. ET (1915 GMT), off an earlier low of $1,305.23.

Oil prices regained ground, rising 3 percent, while investors refocused on potential supply outages and drawdowns in crude.

U.S. crude oil futures <CLc1> settled up 3.3 percent, or $1.52, at $47.85, while Brent crude <LCOc1> rose 3 percent, or $1.42, at $48.58 per barrel.

Overnight in Asia, MSCI's broadest index of Asia-Pacific shares outside Japan <.MIAPJ0000PUS> ended up 0.5 percent.

(Reporting by Hilary Russ in New York; Additional reporting by Yashaswini Swamynathan in Bengaluru; Herb Lash, Sam Forgione and Barani Krishnan in New York; Michael Holden in London and Elizabeth Piper in Brussels; Editing by Dan Grebler and Chizu Nomiyama)