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* U.S. manufacturing sector growth slowing -ISM

* Senate unveils $1 trillion infrastructure bill

* Square rises on $29 billion Afterpay deal

* Focus on services sector data, jobs report this week

* Indexes: Dow off 0.28%, S&P down 0.18%, Nasdaq adds 0.06%

NEW YORK, Aug 2 (Reuters) - The S&P 500 Index closed slightly lower on Monday after erasing early gains as worries about the Delta variant of the coronavirus and a slowing U.S. economy overshadowed optimism around more fiscal stimulus and a strong second-quarter earnings season.

Federal Reserve Governor Christopher Waller said late in the session that the Fed could start to reduce its support for the economy by October if the next two monthly jobs reports each show employment rising by 800,000 to 1 million, as he expects.

He also suggested the Fed could start to reduce its monthly bond purchases in September, which could lift yields again - not the best news for the stock market.

Data earlier in the day showed that although U.S. manufacturing grew in July, its pace slowed for a second straight month as spending rotated back to services from goods, and shortages of raw materials persisted.

The softer-than-expected data also sent U.S. bond yields to their lowest since July 20 and knocked the blue-chip Dow off an intra-day record high hit in early trading.

“An issue for the market... is the rise of the growth scare", said Rob Haworth, senior investment strategist at U.S. Bank, "Whether it's more restrictions in China with infections rising in 14 provinces now, or questions about how far is the U.S. going to have to go with mask mandates.”

Only four of the 11 S&P sectors traded higher by market close, among them utilities and real estate , generally considered safe bets at a time of uncertainty.

The Dow Jones Industrial Average fell 97.31 points, or 0.28%, to 34,838.16, the S&P 500 lost 8.1 points, or 0.18%, to 4,387.16 and the Nasdaq Composite added 8.39 points, or 0.06%, to 14,681.07.

Square Inc, the payments firm of Twitter Inc co-founder Jack Dorsey, jumped after it said it would purchase Australian buy now, pay later pioneer Afterpay Ltd for $29 billion.

Automaker Tesla was another bright spot on Monday, with the volatile stock rising 3.3%.

With manufacturing activity data coming in weaker than expected, investor focus now turns to services sector data on Wednesday and the Labor Department's monthly jobs report on Friday.

After mixed quarterly reports from technology behemoths last week, all eyes this week are on earnings from companies including Eli Lilly and Co , CVS Health Corp and General Motors Co.

Volume on U.S. exchanges was 8.80 billion shares, compared with the 9.77 billion average for the full session over the last 20 trading days.

Declining issues outnumbered advancing ones on the NYSE by a 1.07-to-1 ratio; on Nasdaq, a 1.05-to-1 ratio favored advancers.

The S&P 500 posted 76 new 52-week highs and 2 new lows; the Nasdaq Composite recorded 98 new highs and 67 new lows.