* European shares rise, led by Italian banks
* Wall Street climbs with support from financials, tech stocks
* Dollar gains after strong ADP jobs data, Italy weighs on euro
* Oil retreats further from 4-year high as Saudi pumps more
* (Recasts lead with U.S. Treasuries; updates with afternoon trading, oil report)
NEW YORK, Oct 3 (Reuters) - Stock markets around the world were mixed on Wednesday amid signs that Rome would cut budget deficits and decrease its debt in the coming years, while U.S. Treasuries yields hit multi-year highs and the dollar firmed as data pointed to another Federal Reserve rate hike.
On Wall Street, strong early gains, including a record high in the Dow, were whittled down in afternoon trade. Financial stocks gained from a rebound in European markets.
The Dow Jones Industrial Average rose 48.34 points, or 0.18 percent, to 26,822.28, the S&P 500 gained 1.15 points, or 0.04 percent, to 2,924.58 and the Nasdaq Composite added 23.01 points, or 0.29 percent, to 8,022.55.
MSCI's gauge of stocks across the globe lost 0.13 percent.
U.S. Treasury yields reached multiyear peaks, with the 10-year note's yield at its highest since 2014 and maturities at the short end of the curve at decade highs, after economic data bolstered the case for the Fed to raise interest rates in December.
Benchmark 10-year notes last fell 26/32 in price to yield 3.1512 percent. The 30-year bond last fell 58/32 in price to yield 3.306 percent.
The yield on the benchmark 10-year note was on track for its largest daily jump since the U.S. presidential election in November 2016 as U.S. service sector activity hit a 21-year high and the ADP private payrolls data for September came in stronger than expected.
"This is a bigger reaction to economic data than anything we've seen lately," said Gene Tannuzzo, senior portfolio manager at Columbia Threadneedle Investments.
The U.S. dollar also gained after the release of the ADP data, which comes ahead of the more comprehensive non-farm payrolls data on Friday.
"Since today's data came in well above market expectations, this release is likely to inspire other forecasters to revise their forecasts higher," said Ward McCarthy, money market economist at Jefferies.
Stock markets around the world initially rose after a report in the Corriere della Serra newspaper - later confirmed to Reuters by a government source - said Italy's deficit would fall to 2.2 percent of gross domestic product in 2020 and to 2 percent in 2021 from the 2.4 percent earlier outlined. That relieved some concerns that Italian budget deficits could deepen its debt problems and stoke conflict with the European Union .
Italian 10-year borrowing costs eased off 4-1/2-year highs , after jumping 50 basis points since budget details emerged last Thursday. Two-year yields fell 10 bps.
The improved mood toward Italy also reduced the premium investors demand for holding Italian risk relative to that of safer Germany to around 290 bps, down from a five-year high over 300 bps on Tuesday, and sapped demand for safe-haven assets such as German bonds and Swiss franc.
"Today, so far, has been better-than-expected performance out of Europe," said Michael Antonelli, managing director of institutional sales trading at Robert W. Baird in Milwaukee.
The pan-European equity index rose 0.5 percent, while the Milan bourse jumped more than one percent. The moves were led by an initial 3.1 percent bounce in Italian banks.
Lingering concerns about Italys budget negotiations continued to weigh on the euro, which was down 0.3 percent to $1.1517. The single currency hit a six-week trough of $1.1506 on Tuesday after an Italian lawmaker said his country might be better off with its "own currency."
In oil, Brent crude rose to a four-year high as the market focused on upcoming U.S. sanctions on Iran while shrugging off the year's largest weekly build in U.S. crude stockpiles and reports of higher Saudi Arabian and Russian production.
U.S. crude rose 1.57 percent to $76.41 per barrel and Brent settled at $86.29, up 1.76 percent on the day.
(Reporting by Laila Kearney Additional reporting by Swati Pandey in Sydney, Karen Brettell in New York Editing by Leslie Adler Editing by Mark Heinrich and Frances Kerry)