NEW YORK (Reuters) - U.S. stocks rose on Monday, following a sharp sell-off in the prior session, after U.S. President Donald Trump predicted a trade deal with China, cooling investor concerns after a ramp-up in rhetoric derailed markets last week.

Following the G7 summit of world leaders in Biarritz, France, Trump said he believed China was sincere about the desire to reach a deal, citing what he described as increasing economic pressure on Beijing and job losses there.

Shares of tariff-sensitive companies rose in response. Apple Inc's AAPL.O 1.90% gain provided the biggest boost to each of the major indexes.

Chipmakers, which are heavily reliant upon China for revenue, also rose. The Philadelphia Semiconductor index .SOX added 0.86% after slumping more than 4% on Friday.

Still, market participants said the rebound paled in comparison to last week’s decline, and they expected recent volatility to continue.

“The markets are telling us something very important with this pricing action today. We are seeing some gains across the board for the Nasdaq S&P and Dow, but we are also seeing a very significant downtick in volume,” said Peter Kenny, founder of Kenny’s Commentary LLC and Strategic Board Solutions LLC in New York.

“This is not a healthy bounce and it is across virtually all the major indexes. So it is an indication the momentum for U.S. equities remains biased to the downside,” Kenny said.

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The Dow Jones Industrial Average .DJI rose 269.93 points, or 1.05%, to 25,898.83, the S&P 500 .SPX gained 31.27 points, or 1.10%, to 2,878.38, and the Nasdaq Composite .IXIC added 101.97 points, or 1.32%, to 7,853.74.

Commerce Department data showed new orders for key U.S.-made capital goods rose modestly in July, while shipments fell by the most in nearly three years. The data could provide the Federal Reserve with more fuel to cut interest rates again when policymakers meet next month.

Concerns about the global economy slipping into recession and uncertainty over the pace of U.S. interest rate cuts have created some anxiety about how long the current U.S. expansion will last. The S&P 500 is off more than 5% from the record high hit in late July after suffering its longest run of weekly declines since May.

Even with Monday's broad gains, with each of the major S&P 500 sectors rising, Wall Street's fear gauge, the CBOE Volatility index .VIX, hit its highest level in more than a week earlier in the session.

Among other stocks, Celgene Corp CELG.O rose 3.20% after Amgen Inc AMGN.O said it would buy the company's psoriasis drug Otezla, clearing the way for Bristol-Myers Squibb Co BMY.N to go ahead with its $74 billion deal for Celgene. Shares of Bristol-Myers rose 3.28%

Advancing issues outnumbered declining ones on the NYSE by a 1.66-to-1 ratio; on Nasdaq, a 1.74-to-1 ratio favored advancers.

The S&P 500 posted four new 52-week highs and 17 new lows; the Nasdaq Composite recorded 17 new highs and 134 new lows.

About 5.71 billion shares changed hands in U.S. exchanges, compared with the 7.57 billion daily average over the last 20 sessions.