* US-China still 'very far apart' on trade-U.S. ambassador
* Mexico does not sees NAFTA deal coming this week
* April retail sales up 0.3 pct, vs. 0.8 pct rise in March
* Home Depot drops as sales misses estimate, drags Lowe's
* Indexes down: Dow 0.7 pct, S&P 0.75 pct, Nasdaq 0.98 pct
May 15 (Reuters) - Wall Street indexes fell on Tuesday as investors worried about a lack of progress in U.S.-China trade talks and Treasury yields rose after U.S. retail sales data indicated rising inflation.
The United States and China are still "very far apart" on resolving trade frictions, U.S. Ambassador to China Terry Branstad said, as a second round of high-level talks were set to begin in Washington.
Adding to the trade woes, Mexico's economy minister Ildefonso Guajardo said he does not expect to meet a deadline this Thursday to reach a new North American Free Trade Agreement that could be presented to the U.S. Congress.
U.S. retail sales increased a moderate 0.3 percent in April, compared with an upwardly revised 0.8 percent surge in March, as rising gasoline prices weighed on discretionary spending, the Commerce Department said.
However, the rise in core retail sales, which excluded automobiles, gasoline, building materials and food services, showed consumer spending appeared on track to accelerate after slowing sharply in the first quarter.
Following the data, benchmark U.S. Treasury yield hit 3.037 percent, a key breakout level, before gaining further to 3.058 percent, their highest since July 2011.
"It's a combination of less good news from China trade situation, a bit of a seasonal miss on Home Depot and tick up in the yield on 10-year that conspires to be the story ... and unraveled some of that positive feeling we had yesterday," said Art Hogan, chief market strategist at B. Riley FBR in Boston.
"The (retail sales) data is impressive, the yield on the 10-year is reflective of that, and that we get further noise on 3 percent and that becomes an issue."
The losses were broad based with all the 11 major S&P sectors and all the 30 Dow components in the red.
Home Depot Inc slipped 1.7 percent in premarket trading after the No.1 U.S. home improvement chain missed Wall Street forecasts for sales at established stores as an unusually long winter hit demand for typical spring products.
Smaller rival Lowe's was down 0.8 percent.
At 9:46 a.m. EDT the Dow Jones Industrial Average was down 175.28 points, or 0.70 percent, at 24,724.13, the S&P 500 was down 20.54 points, or 0.75 percent, at 2,709.59 and the Nasdaq Composite was down 72.66 points, or 0.98 percent, at 7,338.66.
Agilent Technologies dropped 9.1 percent after posting a disappointing quarterly forecast late on Monday.
Ford dipped 0.8 percent after Piper Jaffray cut its rating to "neutral" on the automaker's shares.
Declining issues outnumbered advancers for a 3.96-to-1 ratio on the NYSE. Declining issues outnumbered advancers for a 1.98-to-1 ratio on the Nasdaq.
The S&P index recorded 1 new 52-week highs and 5 new lows, while the Nasdaq recorded 21 new highs and 20 new lows. (Reporting by Medha Singh in Bengaluru; Editing by Saumyadeb Chakrabarty and Arun Koyyur)