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* China willing to reach agreement with U.S. - Xinhua
* Apple rises as brokerage sees higher iPhone demand
* Indexes up: Dow 0.6%, S&P 500 0.6%, Nasdaq 0.6% (Updates to close)
By Caroline Valetkevitch
NEW YORK, Oct 10 (Reuters) - U.S. stocks rose on Thursday on hopes that top-level U.S.-China trade talks would yield at least a partial deal, while a jump in Apple's shares also boosted the market.
Top U.S. and Chinese negotiators met on Thursday for the first time since late July to try to find a way out of a 15-month trade war.
After the bell, the S&P e-minis jumped and were last up about 1%, as U.S. President Donald Trump said the talks with China went "very well today."
He had tweeted earlier that he would meet with China's top negotiator, Vice Premier Liu He at the White House on Friday.
Chinese officials had indicated more willingness to negotiate, according to a Chinese state news agency Xinhua report, while a senior U.S. Chamber of Commerce official said U.S. and Chinese negotiators were working toward an "early harvest" of confidence-building agreements, including one to avoid currency manipulation.
Cyclical groups including energy, financials, industrials and materials were the day's best-performing sectors, while the Dow Jones transportation average jumped 1.3%.
"There's still some hope that something happens here," said Bucky Hellwig, senior vice president at BB&T Wealth Management in Birmingham, Alabama.
"But there seems to be an acceptance that this thing may not be finished."
Apple Inc jumped 1.3% after Longbow Research upgraded the company's stock to "buy", citing higher iPhone 11 demand.
The Dow Jones Industrial Average rose 150.66 points, or 0.57%, to 26,496.67, the S&P 500 gained 18.73 points, or 0.64%, to 2,938.13 and the Nasdaq Composite added 47.04 points, or 0.6%, to 7,950.78.
Stocks have been volatile in recent weeks because of weak economic indicators showing a contraction in U.S. manufacturing and a bleak reading on business activity, bolstering bets of another interest rate cut by the Federal Reserve to combat a slowdown.
Data on Thursday showed U.S. consumer prices were unchanged in September, while underlying inflation retreated.
Among other stocks, Delta Air Lines Inc fell 1.5% after the carrier forecast disappointing current-quarter profit.
Focus will shift even further to earnings next week when the reporting period begins in earnest. Analysts are forecasting a 3.1% decline in earnings for the third quarter from a year ago, based on IBES data from Refinitiv, and that could mark a recent low point in year-over-year quarterly changes.
Advancing issues outnumbered declining ones on the NYSE by a 1.71-to-1 ratio; on Nasdaq, a 1.27-to-1 ratio favored advancers.
The S&P 500 posted six new 52-week highs and four new lows; the Nasdaq Composite recorded 15 new highs and 128 new lows.
Volume on U.S. exchanges was 6.16 billion shares, compared to the roughly 7 billion average for the full session over the last 20 trading days. (Additional reporting by Shreyashi Sanyal and Medha Singh in Bengaluru; Editing by Shounak Dasgupta, Nick Zieminski and Tom Brown)