US STOCKS-Wall Street muted on doubts over progress in U.S.-China trade deal

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* S&P, Dow set for third straight session of losses

* Energy shares up, tracking oil prices

* TD Ameritrade surges as Schwab in talks to buy company - CNBC

* Indexes down: Dow 0.02%, S&P 0.02%, Nasdaq 0.1% (Updates to late afternoon, adds commentary, New York dateline, changes byline,)

By Sinéad Carew

Nov 21 (Reuters) - The S&P 500 and Dow indexes treaded water on Thursday as mixed headlines on U.S.-China relations and a diplomatic row over the Hong Kong protests added to uncertainty over the timing of a "phase one" trade deal.

The U.S. House of Representatives passed two bills to back protesters in Hong Kong and send a warning to China about human rights, a measure which angered Beijing.

But China has invited top U.S. trade negotiators for a new round of face-to-face talks in Beijing, the Wall Street Journal reported on Thursday, citing unnamed sources, adding Beijing hopes the round of talks can take place before next Thursday's Thanksgiving holiday in the United States.

This was the day after stocks sold off on a report that a Phase 1 U.S.-China trade deal was not likely to happen this year. As a result investors were sticking to the sidelines for fear of missing out if relations were to improve, but keeping in mind that Wall Street's indexes were still near record highs.

"The fulcrum of this optimism see-saw is the prospects for the phase 1 trade agreement. Investors are pulling petals from a daisy saying, 'it'll happen this year, it won't,'" said Sam Stovall, chief investment strategist at CFRA Research in New York.

"They are basically saying we've pushed this as far as we can. Valuations appear stretched at 18.5 times forward earnings compared with the 20-year average forward P/E Of 16.5," he said.

At 2:47 p.m. ET, the Dow Jones Industrial Average fell 6.89 points, or 0.02%, to 27,814.2, the S&P 500 lost 0.61 points, or 0.02%, to 3,107.85 and the Nasdaq Composite dropped 8.62 points, or 0.1%, to 8,518.11.

Six out of the S&P 500's 11 major industry sectors rose on the day with energy showing the biggest gain at 1.4% as oil prices rose on hopes that the OPEC and its allies were likely to extend output cuts until mid-2020..

Real estate showed the biggest decline at 1% and technology was the biggest drag on the benchmark index.

Shares in TD Ameritrade Holding Corp surged 18% after CNBC reported bigger rival Charles Schwab Corp was in talks to buy the discount brokerage. Schwab's shares gained 6.8%.

Tiffany & Co gained about 2.3% after a Reuters report that LVMH persuaded the jewelry chain to allow it to access its books following a raised bid.

Economic data was mixed on Thursday. The number of Americans filing applications for unemployment benefits was unexpectedly unchanged at a five-month high last week, suggesting some softening in the labor market.

But U.S. home sales increased more than expected in October and house prices rose at the fastest pace in more than two years amid lower mortgage rates and a shortage of properties for sale.

Declining issues outnumbered advancing ones on the NYSE by a 1.44-to-1 ratio; on Nasdaq, a 1.26-to-1 ratio favored decliners.

The S&P 500 posted 11 new 52-week highs and 3 new lows; the Nasdaq Composite recorded 46 new highs and 82 new lows. (Additional reporting by Manas Mishra and Uday Sampath Kumar in Bengaluru; Editing by Arun Koyyur and Nick Zieminski)