* S&P 500 pares gains after hitting record
* Euro firms against dollar
* European shares rise on ECB stimulus hopes (Adds close of European markets, drop in Apple shares)
By Sam Forgione
NEW YORK, Sept 3 (Reuters) - Equity markets worldwide rose on Wednesday, with the S&P 500 hitting a record high on hopes a resolution would be reached between Ukraine and Russia, while the euro rebounded from a one-year low against the dollar on expectations for more European Central Bank stimulus.
The S&P 500 index pared its gains in afternoon trading on some doubts over a resolution over Ukraine and a drop in Apple shares, which also dragged down the tech-heavy Nasdaq index. Speculation of a possible cease-fire in eastern Ukraine still limited bets on safe-haven U.S. Treasuries. Oil prices rose.
The euro rose as high as $1.31600 after hitting a one-year low of $1.3110 on Tuesday. The dollar weakened against the Russian rouble, while the dollar-denominated RTS stock index gained 5.2 percent on the day.
Russian President Vladimir Putin said on Wednesday a deal to end fighting in eastern Ukraine could be reached this week in Kiev's conflict with pro-Russian rebels, but the Kremlin denied any actual truce deal.
The situation is still fraught, with Ukraine's prime minister saying Wednesday that Putin's proposals were an attempt to deceive the West ahead of a NATO summit this week. Analysts said many details about a peace plan need to be clarified.
"I think that for now (market) players will sit and wait. Of course if the conflict finally ceases, the (stock) indexes could rise another 10 percent," said Andrei Bachurin, chief trader at Renaissance Capital.
European shares rose ahead of the ECB's policy meeting on Thursday on speculation the central bank might launch an asset-purchase program to boost inflation in the euro zone.
MSCI's all-country world index of 45 countries was last up 1.93 points or 0.45 percent, at 433.1, while the pan-European FTSEurofirst 300 index closed up 0.69 percent, at 1,385.49.
"The ECB still has plenty of ammunition left," said Romain Boscher, global head of equities management at Amundi, which oversees $1.08 trillion. "The prospect of further action from the central bank remains very supportive for risky assets such as equities."
The Dow Jones industrial average was last up 34.23 points, or 0.2 percent, to 17,101.79, the S&P 500 rose up 0.52 points, or 0.03 percent, to 2,002.8 and the Nasdaq Composite fell 18.07 points, or 0.39 percent, to 4,580.12.
Apple shares were last down 3.3 percent at $99.92 as it grappled with a possible security breach into its iCloud service a week before a crucial launch of its new iPhone.
Brent crude for October delivery was last up $1.92, or up 1.91 percent, at $102.26 a barrel. U.S. crude was last up $2.26, or up 2.43 percent, at $95.14 per barrel.
U.S. government bond prices inched higher, with the 10-year note up 1/32 in price to yield 2.4140 percent. (Additional reporting by Francesco Canepa in London and Richard Leong and Ryan Vlastelica in New York, Editing by Chizu Nomiyama)