* U.S. stocks up as oil rebounds
* Italy, Spain fall on Greece concerns, austerity issues
* Euro zone data shows slight growth in January (Updates with close of U.S. markets)
By Chuck Mikolajczak
NEW YORK, Feb 2 (Reuters) - Global equity markets rose sharply in choppy trade on Monday on a late rally fueled by hopes for a deal on Greek debt, with a rebound in oil prices also helping to lift U.S. stocks.
Markets rallied in the last hour of trading after new Greek Finance Minister Yanis Varoufakis told the Financial Times Greece has proposed ending a standoff with its international creditors by swapping its outstanding debt for new growth-linked bonds. A source told Reuters the plan has not yet been discussed with the European Central Bank or EU officials.
Crude oil prices rose, building on a rally in the prior session as some investors bet a seven-month drop in the commodity may be nearing an end. U.S. crude settled up 2.76 percent at $49.57 a barrel while Brent settled up 3.32 percent at $54.75.
"Markets are finding some comfort in the fact there is a dialogue that has the potential to lead to something other than a Grexit, that is a constructive narrative for equity markets, not just in the U.S. but globally," said Peter Kenny, chief market strategist at Clearpool Group in New York.
"That coupled with the rebound in crude has helped take the attention away from those two drivers of risk aversion."
Trading was choppy for much of the session after U.S. economic data showed consumer spending fell and construction spending rose less than expected in December, while an industry report pointed to slowing in the manufacturing sector in January.
The S&P 500 is still down more than 3 percent from its record high set on Dec. 29, pulled lower by a lackluster earnings season and data showing a U.S. economy growing at a slower pace than investors had been anticipating.
Stocks in Europe were mixed, with declines in Spanish and Italian shares as Greece seeks to end its existing debt deal and data pointed to weak January growth in euro zone factory activity. Spain and Italy have seen a rise in popularity of anti-austerity parties.
On Saturday, tens of thousands marched in Madrid in the biggest show of support yet for Spanish anti-austerity party Podemos, whose policies have drawn comparisons with the Syriza party that now governs Greece.
Greece's leftist government began its drive to persuade a skeptical Europe to accept a new debt agreement. The finance minister and new Prime Minister Alexis Tsipras are touring European capitals in a diplomatic offensive to replace Greece's bailout accord.
MSCI's all-country world stock index, a measure of stock performance in 45 countries, rose 0.9 percent. The FTSEurofirst 300 index of top European shares closed up 0.2 percent.
The Dow Jones industrial average rose 196.09 points, or 1.14 percent, to 17,361.04, the S&P 500 gained 25.86 points, or 1.3 percent, to 2,020.85 and the Nasdaq Composite added 41.45 points, or 0.89 percent, to 4,676.69.
The dollar weakened in the wake of the economic data, with the U.S. dollar index last off 0.3 percent. The benchmark 10-year U.S. Treasury note was up 4/32, the yield at 1.6676 percent.
Reporting by Chuck Mikolajczak; Editing by Dan Grebler