(Updates through mid-afternoon trading, adds detail on GE)
By David Randall
NEW YORK, Oct 30 (Reuters) - Broad gains in the U.S. equity market turned global stocks higher on Tuesday after President Donald Trump said a "great deal" could be struck with China that would relieve fears of a growing trade war between the world's two largest economies.
The euro wallowed near a 10-week low of $1.1352 as the dollar climbed to a 2 1/2-month peak against a basket of the world's top six currencies.
MSCI's gauge of stocks across the globe gained 0.31 percent. Still, the index is down nearly 10 percent for the month.
Investors remained cautious despite the modest global gains.
"At this point, nobody can say the equity market is bottoming out. Global investor sentiment remains shaky," said Yasuo Sakuma, chief investment officer at Libra Investments in Tokyo.
Market participants also kept hopes in check regarding trade.
"We don't see the trade war being resolved any time soon," said Rabobank's senior macroeconomic strategist Teeuwe Mevissen. "And it comes at a time when we see all the sentiment indicators in the euro zone but also in the U.S., too, cooling down."
Trump said during an interview with Fox News he thought there could be an agreement with China on trade, but said he had billions of dollars worth of new tariffs ready to be imposed if a deal was not possible.
The Dow Jones Industrial Average rose 189.08 points, or 0.77 percent, to 24,632, the S&P 500 gained 14.5 points, or 0.55 percent, to 2,655.75 and the Nasdaq Composite added 33.79 points, or 0.48 percent, to 7,084.08.
The gains were broad in the U.S., with 9 of the 11 sectors of the benchmark S&P index up for the day. Trade-sensitive industrial shares rose nearly 0.7 percent in mid-afternoon trading.
General Electric Co, however, fell 11 percent. GE slashed its quarterly dividend to a penny a share, promised to restructure its power unit and said it faced a deeper accounting probe.
Meanwhile, data showed the Italian economy had ground to a halt in the third quarter as both domestic demand and trade flows failed to spur growth.
The flat reading was the weakest since the fourth quarter of 2014 and renewed pressure on Italy's government debt in the bond markets.
The pan-European STOXX 600 index rose 0.01 percent.
The chill around China and global trade left emerging- market stocks at an 18-month low, with MSCI's index down for a sixth day in a row.
Oil prices fell more than 1 percent in choppy trading on signs of rising supply and concern global economic growth and fuel demand would be hit by a deepening of the U.S.-China trade dispute.
U.S. crude fell 1.45 percent to $66.07 per barrel and Brent was last at $75.75, down 2.06 percent.
Benchmark 10-year notes last fell 6/32 in price to yield 3.1076 percent, from 3.087 percent late on Monday.
Reporting by David Randall; Editing by Bernadette Baum and Nick Zieminski