US STOCKS-U.S. stocks gain as signs of recovery offset protests, economic worries

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* U.S. factory activity eases off an 11-year low in May

* Target, Walmart shut stores as U.S. protests turn violent

* Coty rises after appointing Chairman Peter Harf as CEO

* Indexes up: Dow 0.35%, S&P 0.48%, Nasdaq 0.73% (Updates to late afternoon, changes dateline, byline)

NEW YORK, June 1 (Reuters) - Wall Street stocks posted modest gains on Monday as signs suggesting the U.S. economy may be on the road to recovery helped soothe jitters over increasingly violent social unrest and rising U.S.-China tensions.

All three major stock indexes began the month less than 1% higher following a strong rally in May.

Market leaders Apple Inc, and Facebook Inc provided the biggest lift to the S&P 500 and the Nasdaq, while Boeing Co provided the blue-chip Dow with its biggest boost.

“What’s really giving people hope are the moves by the central banks, especially the Fed, that prop up the economy and the market,” said Robert Pavlik, chief investment strategist at SlateStone Wealth LLC in New York. “That seems to be the overall theme.”

The White House called for “law and order” as U.S. cities were looted and smoldering after six nights of widespread, violent demonstrations triggered by the death of George Floyd at the hands of police.

“We have seen some headway was far as the coronavirus is concerned and the economy is slowly reopening,” Pavlik added. “But the protests and violence associated with them creates another underlying concern.”

The unrest has prompted retailers such as Target Corp and Walmart Inc to shutter a portion of their stores, while has scaled back deliveries.

Further weighing on sentiment, China has ordered state-owned firms to halt purchases of U.S. soybeans and pork, in retaliation for President Donald Trump’s announcement that he would end special treatment for Hong Kong following China’s move to tighten security measures in the territory.

But economic data gave a boost to investor sentiment, with the Institute for Supply Management’s (ISM) purchasing managers’ index (PMI) showing the contraction of factory activity was slowing, and a decline in construction spending was not as steep as economists feared.

A fuller picture of the economic damage wrought by pandemic-related lockdowns is expected on Friday, when the Labor Department’s jobs report is seen showing a drop of 8 million jobs and an unemployment rate sky-rocketing to 19.7%.

The Dow Jones Industrial Average rose 90.76 points, or 0.36%, to 25,473.87, the S&P 500 gained 14.5 points, or 0.48%, to 3,058.81 and the Nasdaq Composite added 69.73 points, or 0.73%, to 9,559.60.

Of the 11 major sectors in the S&P 500, all but healthcare were in positive territory.

Pfizer Inc dropped 7.0% after the drugmaker’s breast cancer treatment was deemed unlikely to meet the main goal of a late-stage study.

Biotech firms CTI Biopharma Corp and Proteostasis Therapeutics Inc were up 10.8% and 10.7%, respectively, after their potential COVID-19 treatments showed promise.

Meanwhile, rival Gilead Sciences Inc dipped 2.7% following mixed results in a late-stage study of its COVID-19 drug candidate, remdesivir.

Coty Inc jumped 17.5% after the appointment of Chairman Peter Harf as its new chief executive officer.

Advancing issues outnumbered declining ones on the NYSE by a 3.95-to-1 ratio; on Nasdaq, a 2.41-to-1 ratio favored advancers.

The S&P 500 posted 19 new 52-week highs and no new lows; the Nasdaq Composite recorded 89 new highs and eight new lows. (Reporting by Stephen Culp; Editing by Cynthia Osterman)