* 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
* (Updates with U.S. markets open)
By Laila Kearney
NEW YORK, Oct 3 (Reuters) - Stock markets around the world rose and Italian bonds rallied on Wednesday after signs that Rome would cut budget deficits and decrease its debt in the coming years, while new U.S. jobs data supporting a strong U.S. economy boosted the dollar.
U.S. stocks rose at the open, with the Dow Jones Industrial Average opening at a record high, as financial stocks gained from a rebound in European markets.
The Dow Jones Industrial Average rose 156.86 points, or 0.59 percent, to 26,930.8, the S&P 500 gained 12.19 points, or 0.42 percent, to 2,935.62 and the Nasdaq Composite added 28.33 points, or 0.35 percent, to 8,027.87.
MSCI's gauge of stocks across the globe gained 0.22 percent.
"Today, so far, has been better-than-expected performance out of Europe," said Michael Antonelli, managing director, institutional sales trading at Robert W. Baird in Milwaukee, Wisconsin.
Markets lifted 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 relieves 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 towards 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.
The pan-European equity index rose 0.6 percent, while the Milan bourse jumped more than one percent. The moves were led by an initial 3.1 percent bounce in Italian banks. The banks' large government debt holdings make them particularly vulnerable to bond selloffs and have pressured Italian stock markets for months.
The U.S. dollar gained after the release of ADP National Employment Report on Wednesday that showed private employers added 230,000 jobs in September, the most since February. That was more than economists’ expectations of 185,000 jobs.
The stronger-than-expected data comes ahead of the more comprehensive non-farm payrolls data on Friday.
The dollar index rose 0.06 percent.
Lingering concerns about Italy’s budget negotiations continued to weigh on the euro, which was down 0.07 percent to $1.1538. 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."
Uncertainty about Italy has continued to weigh on broader market sentiment, as have worries that a U.S.-China tariff dispute will escalate once Chinese markets reopen after a week-long holiday.
While U.S. President Donald Trump agreed a new trade pact with Mexico and Canada, a disputed clause in the trilateral agreement, forbidding similar deals with "non-market" countries, was seen as raising risks for Sino-U.S. talks.
MSCI's index of Asia-Pacific shares outside Japan slipped 0.2 percent and Japan's Nikkei closed 0.7 percent lower.
China's financial markets will resume trade on Oct. 8, the day Trump and Chinese President Xi Jinping are due to attend G-20 meetings, meaning news could emerge on the trade front.
In oil, prices retreated from session peaks near a four-year high as top exporter Saudi Arabia said it increased output and after Reuters reported that Russia and Saudi Arabia had struck a deal to pump more.
U.S. crude rose 0.17 percent to $75.36 per barrel and Brent was last at $85.20, up 0.47 percent on the day.
Additional reporting by Swati Pandey in Sydney, Karen Brettell in New York Editing by Mark Heinrich and Frances Kerry