* Euro, Italian bonds rebound on budget deficit cut report
* European shares rise led by Italian banks; U.S. to open firmer
* Indian, Indonesian, Turkish currencies hit by oil, inflation pressure
* Oil hovers near four-year highs
* Wall Street set to open higher
* (Updates throughout)
LONDON, Oct 3 (Reuters) - European shares rose and Italian bonds rallied on Wednesday as some of the worries that have rippled across markets this week were soothed by signs Rome was amenable to cutting budget deficits and debt in coming years.
While the euro ceded some earlier gains against the dollar to trade flat on the day, the positive sentiment rippled across the Atlantic where Wall Street looks set for a stronger session.
Markets were lifted on Wednesday by a report in the Milan daily Corriere della Serra - later confirmed to Reuters by an Italian government source - that said the 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 fears that Italy's decision to expand budget deficits well beyond what was agreed by a previous government would deepen its debt problems and stoke conflict with the European Union.
"It's all about Italy today. The news about a possible reduction in budget deficits has been positively taken by all markets," said Bernd Berg, global macro and FX strategist at Woodman Asset Management in Zurich.
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' huge government debt holdings make them particularly vulnerable to bond selloffs and have pressured Italian stock markets for months.
Futures for the U.S. S&P 500 and the Dow were up around 0.3-0.4 percent.
The euro firmed 0.3 percent before yielding gains and trading flat around $1.1543, as the dollar cut earlier losses. 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."
However the euro held onto gains against the Swiss franc and yen, rising around 0.4 percent .
"That the Italian government is trying to appease its EU partners can be seen as a step in the right direction and therefore justifies some euro-positive reaction," Thu Lan Nguyen, a FX strategist at Commerzbank, said.
But, she added, "the devil is in the details. The euro's recovery will only continue if the new fiscal plans are also feasible."
Broader world market sentiment remains jittery, partly because of the bellicose rhetoric still emerging from the populist coalition government in Rome, but also due to fears that a Sino-U.S. tariff dispute will escalate once China reopens 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.
Volatility in U.S. tech shares is also making investors wary, with Facebook down almost 6 percent in the past three sessions after disclosing its worst security breach ever.
World shares were flat near two-week lows while 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 are closed and will resume trade on Oct. 8. That's the day Trump and Chinese President Xi Jinping are due to attend G-20 meetings, meaning news could emerge on the trade front.
The dollar index, measuring the greenback against a basket of major currencies, inched higher but is off Tuesday's six-week high of 95.744.
That gave some relief to emerging currencies but the Indian rupee hit a new record low and the Indonesian rupiah touched a more than 20-year low as oil prices near four-year highs weighed.
Turkey's lira also weakened 1.3 percent as the country, another oil importer, posted data showing inflation surpassing 25 percent. That increases pressure for another interest rate rise after a 625 bps move in August.
Woodman Asset Management's Berg said, however, that the worst looked to be over for Turkey. "The currency has appreciated and the central bank has hiked rates aggressively so...towards the end of the year, inflation numbers should stabilize and, to me, the worst of the currency crisis is over."
Brent crude inched up to $84.89 per barrel, close to four-year highs of $85.45 touched earlier this week.
(Additional reporting by Swati Pandey in Sydney Editing by Mark Heinrich)