* U.S. and China to resume trade talks - Bloomberg
* Apple shares up over 2 pct in postmarket trading after results
* S&P 500, Dow post biggest monthly percentage gains since Jan
* Core PCE inflation hovers near Fed target
* Indexes up: Dow 0.43 pct, S&P 0.49 pct, Nasdaq 0.55 pct (Updates to market close)
By Stephen Culp
NEW YORK, July 31 (Reuters) - U.S. stocks rebounded on Tuesday, boosted by gains in industrial shares following reports of renewed trade negotiations between the United States and China.
Both the S&P 500 and the Dow Jones Industrial Average posted their biggest monthly percentage gains since January, when markets hit peak levels.
The markets were buoyed by a Bloomberg report bloom.bg/2mZgU3V that U.S. Treasury Secretary Steven Mnuchin and Chinese Vice Premier Liu He are exploring ways to cool down the tariff war brewing between the world's two largest economies.
The trade-sensitive industrial sector led the S&P 500 and the Dow industrials higher, rising 2.1 percent a day after a broad sell-off in technology stocks pulled markets lower.
"It's a little bit of buying the dip. We've seen it before," said Paul Nolte, portfolio manager at Kingsview Asset Management in Chicago. "What has happened in the past is ... the market would rebound three or four weeks later and hit all-time highs again."
Apple Inc shares were up over 2 percent in aftermarket trading after posting results that topped Wall Street expectations, driven by sales of higher-priced iPhones.
Investors are eyeing the stock's advance as the company closes in on $1 trillion in market value.
The U.S. Federal Reserve meets this week and is expected to leave interest rates unchanged, but robust economic data and rising inflation will likely keep it on track for two more rate hikes this year.
A report from the Commerce Department showed a 1.9 percent increase in the core PCE price index, hewing closely to the Fed's 2 percent inflation target.
The Dow Jones Industrial Average rose 108.36 points, or 0.43 percent, to 25,415.19, the S&P 500 gained 13.69 points, or 0.49 percent, to 2,816.29 and the Nasdaq Composite added 41.79 points, or 0.55 percent, to 7,671.79.
The second-quarter reporting season remains in full swing, and analysts now expect second-quarter profits for S&P 500 companies to have increased 22.9 percent from last year, up from the 20.7 increase seen on July 1.
Eight of the 11 major sectors of the S&P 500 ended the session in positive territory.
Healthcare stocks provided a boost to all three major U.S. indexes following positive results, with the S&P health sector rising 1.0 percent.
Drugmaker Pfizer Inc beat second-quarter estimates but lowered its full-year revenue forecast. The stock closed up 3.5 percent.
CBS Corp reversed its slide, rising 2.7 percent after Les Moonves survived as the company's chief executive following the board's decision to select an outside counsel to investigate claims of sexual harassment.
Shares of Chipotle Mexican Grill dropped 6.8 percent after reports of customers becoming ill prompted the closing of an Ohio restaurant.
Advancing issues outnumbered declining ones on the NYSE by a 2.15-to-1 ratio; on Nasdaq, a 1.82-to-1 ratio favored advancers.
The S&P 500 posted 21 new 52-week highs and two new lows; the Nasdaq Composite recorded 39 new highs and 73 new lows.
Volume on U.S. exchanges was 7.26 billion shares, compared with the 6.06 billion-share average over the last 20 trading days. (Reporting by Stephen Culp; editing by Jonathan Oatis)