* S&P 500 ends lower after hitting record
* Euro firms against dollar
* European shares rise on ECB stimulus hopes (Adds close of U.S. markets)
By Sam Forgione
NEW YORK, Sept 3 (Reuters) - An index of stocks worldwide rose on Wednesday after Ukraine and Russia took steps toward a ceasefire and traders eyed potential European Central Bank stimulus, while the S&P 500 ended lower after hitting a record high, partly on a drop in Apple shares.
European shares gained on hopes of a resolution of the Ukrainian crisis, while skepticism about such progress weighed on U.S. shares as the day proceeded, along with the decline in Apple stock. Safe-haven U.S. Treasuries yields fell from three-week highs on doubts over the peace talks.
The euro firmed against the dollar and rose as high as $1.31600 after hitting a one-year low of $1.3110 on Tuesday on the potential for more ECB stimulus. The dollar weakened against the Russian rouble, while the dollar-denominated RTS stock index gained 5.2 percent on the day.
"There is certainly some skepticism about the validity of a permanent ceasefire in the Ukraine," said Robert Francello, head trader at Apex Capital in San Francisco.
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 there had been any actual truce deal.
The situation was still fraught, with Ukraine's prime minister saying on 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.
European shares rose ahead of the ECB's policy meeting on Thursday on the talk of a Russia-Ukraine ceasefire and 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 1.81 points or 0.42 percent, at 432.98, while the pan-European FTSEurofirst 300 index closed up 9.56 points, or 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. "The prospect of further action from the central bank remains very supportive for risky assets such as equities."
The Dow Jones industrial average pared gains to close up 10.72 points, or 0.06 percent, at 17,078.28, while the S&P 500 fell 1.56 points, or 0.08 percent, to 2,000.72. The Nasdaq Composite fell 25.62 points, or 0.56 percent, to 4,572.57.
Apple shares closed down 4.2 percent at $98.94 as it grappled with a possible security breach of its iCloud service a week before the crucial launch of its new iPhone.
Brent crude for October delivery settled up $2.43 at $102.77 a barrel. U.S. crude settled up $2.66, at $95.54 per barrel.
Benchmark 10-year U.S. Treasury notes were last up 6/32 in price to yield 2.3980 percent. (Additional reporting by Francesco Canepa in London and Richard Leong and Ryan Vlastelica in New York; Editing by Chizu Nomiyama and Jonathan Oatis)