* Italian stocks slump, yields rise as political worries return
* Euro falls back, give dollar boost after Fed hike
* Oil prices near four-year high as Iran sanctions loom
* Graphic: World FX rates in 2018 tmsnrt.rs/2egbfVh (Changes byline, dateline to NEW YORK; adds Wall Street open, higher dollar; updates throughout)
By Hilary Russ
NEW YORK, Sept 27 (Reuters) - The U.S. dollar rose to touch a one-week high against a basket of major currencies on Thursday following a hike in U.S. interest rates, while a robust economy and surging shares of Apple Inc and Amazon.com Inc boosted the U.S. stock market.
The Federal Reserve on Wednesday raised rates for the third time this year, indicating its confidence in the U.S. economy.
That sentiment carried the dollar higher into a second day and dented the euro, which was further pressured by worries about Italy's budget.
"The Fed is moving faster than most central banks and that's dollar-supportive," said Erik Nelson, currency strategist, at Wells Fargo Securities in New York.
The dollar index, tracking it against six major currencies, rose 0.68 percent, while the euro dipped 0.6 percent to $1.1668.
The greenback hit a two-week peak against the Swiss franc and Canadian dollar.
On Wall Street, the Dow Jones Industrial Average rose 117.28 points, or 0.44 percent, to 26,502.56, the S&P 500 gained 15.89 points, or 0.55 percent, to 2,921.86 and the Nasdaq Composite added 68.42 points, or 0.86 percent, to 8,058.79.
Apple rose 2.5 percent, the biggest boost to the three main indexes after JP Morgan started coverage of the stock with an "overweight" rating.
Amazon.com rose 1.5 percent after brokerage Stifel talked up its businesses.
MSCI's gauge of stocks across the globe gained 0.17 percent.
Reports that Italy's long-awaited budget was facing delay initially dented European shares, which then recovered. The pan-European FTSEurofirst 300 index rose 0.48 percent.
Italy's main Milan bourse slumped as much as 2 percent , and was last down 0.6 percent, with the country's big banks sinking even more as the country's borrowing costs hit a three-week high in the government bond markets.
Rome confirmed that a cabinet meeting over budget targets was still planned for later, dismissing an earlier report in the Corriere della Sera newspaper that it could be delayed.
Still, Italy's economic ministry was forced to deny that its chief Giovanni Tria, an academic who doesn't belong to any one party, had threatened to resign.
"It is very fluid and it is changing by the minute it seems," head of EMEA macro strategy at State Street Tim Graf said.
"Even if things get resolved positively today, Italy is not a situation that is going to go away," he added, pointing to the growing popularity of the country's fractious anti-establishment coalition government.
Japan's Nikkei briefly touched an eight-month high as signs that the United States may not impose further tariffs on Japanese automotive products for now lifted carmakers, though the index eventually ended down nearly 1 percent.
Benchmark U.S. 10-year notes last fell 2/32 in price to yield 3.0667 percent, from 3.061 percent late Wednesday.
Oil edged higher, driven by the prospect of a shortfall in global supply once U.S. sanctions against major crude exporter Iran come into force in just five weeks' time.
U.S. crude rose 0.43 percent to $71.88 per barrel and Brent was last at $81.01, up 0.27 percent.
Additional reporting by Marc Jones and Amanda Cooper in London, Amy Caren Daniel in Bengaluru and Gertrude Chavez-Dreyfuss in New York; Editing by Bernadette Baum