* Euro bounces higher in volatile session, supports Brent
* French banks agree to roll over Greek debt holdings
* U.S. bank shares up after global capital rules announced (Updates prices, adds comment)
By Rodrigo Campos
NEW YORK, June 27 (Reuters) - U.S. stocks led global shares higher on Monday and the euro rallied against the U.S. dollar on increasing confidence the Greek parliament will pass an unpopular austerity plan and as French banks outlined an agreement to roll over Greek debt.
Treasury prices fell as the news from Europe lured investors into riskier assets, while low yields in the government's sale of two-year notes discouraged some potential buyers.
Bank shares were among top gainers in U.S. markets, which rebounded following three days of losses after regulators announced global capital rules that were not as harsh as previously feared. For details see [ID:nN1E75Q0N3].
"We don't see this being the start of a major rally but this is welcome strength in the market and hopefully a welcome short-term bottom," said Tim Ghriskey, chief investment officer of Solaris Asset Management in Bedford Hills, New York.
He said financials were "a very oversold group" that was due for a bounce.
Greek lawmakers were to begin debating on Monday evening a 28 billion euro ($40 billion) package of measures to increase taxes and cut fiscal spending that is critical to winning a new round of international funding to keep the country afloat. [ID:nLDE75P0BM].
"As long as the Greek Parliament votes 'Yes' this week on an austerity plan, stocks are going to go up," said Cary Leahey, economist and managing director at Decision Economics in New York.
French banks, among the most exposed to the Greek debt crisis, have reached an outline agreement to roll over holdings of maturing Greek bonds. French President Nicolas Sarkozy confirmed the breakthrough on Monday and German bankers voiced their interest in the "French model." [ID:nL6E7HR0GU]
On Saturday, global banking regulators in Basel agreed that the biggest banks globally will need to boost their ratios of common equity to risk-weighted assets by up to 2.5 percentage points, less than the 3 percentage points some investors had feared. [ID:nLDE75O053]
The Dow Jones industrial average <.DJI> gained 159.24 points, or 1.33 percent, to 12,093.82. The S&P 500 <.SPX> rose 15.93 points, or 1.26 percent, to 1,284.38. The Nasdaq Composite <.IXIC> added 42.08 points, or 1.59 percent, to 2,694.97.
The S&P financial index <.GSPF> was up 1.4 percent and an index of large U.S. bank stocks <.BKX> rose 1.6 percent.
Global stocks as measured by MSCI <.MIWD00000PUS> were up 0.5 percent for the day.
The FTSEurofirst 300 <.FTEU3> index of top European shares closed up 0.05 percent at 1,074.67 after hitting its lowest level since mid-March on Friday.
U.S. Treasuries fell as shrinking worries over a Greek default reduced safe-haven demand for U.S. government debt. A sale of two-year notes with a yield of less than half a percent further discouraged buyers.
Benchmark 10-year U.S. Treasury notes
"It was a relatively weak auction, almost certainly because two-year rates are within shouting distance of the all-time rate lows set in November 2010," RBS head of Treasury strategy William O'Donnell said in a note to clients.
EURO UP, OIL WEAK
The euro rallied against the U.S. dollar as investors became optimistic the austerity vote will pass in Greece's parliament and the euro zone member can avoid a default on its debt.
The euro had been swinging between gains and losses throughout the global session, responding to each headline or market rumor on the Greek vote, traders said.
"I think the vote will pass or we would be seeing a huge sell-off," said Kathy Lien, director of currency research at GFT Forex in New York. "The fate of the euro/dollar hinges on the outcome of the vote."
The single currency
U.S. crude oil futures
Brent crude futures were 85 cents higher at $105.97 a barrel by 1838 GMT, with the session low at $102.28. U.S. light crude futures fell 56 cents to $90.60 a barrel, after touching lows of $89.61 earlier. (Reporting by Rodrigo Campos; Additional reporting by Edward Krudy, Nick Olivari and Ellen Freilich; Editing by Dan Grebler)