* 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
* Futures down: Dow 0.59 pct, S&P 0.53 pct, Nasdaq 0.83 pct
By Medha Singh
May 15 (Reuters) - U.S. stock index futures dropped on Tuesday as investors were worried about a lack of progress in U.S.-China trade talks and assessed U.S. retail sales data that showed moderate gains last month.
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 yields hit 3.037 percent, a key breakout level, before gaining further to 3.043 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."
Shares of Home Depot Inc slipped 2.5 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 1.7 percent.
At 9:09 a.m. ET, Dow e-minis were down 147 points, or 0.59 percent. S&P 500 e-minis were down 14.5 points, or 0.53 percent and Nasdaq 100 e-minis were down 58 points, or 0.83 percent.
Even oil prices, which have helped boost the stock market in recent days, touching a 3-1/2-year high, did not offer succor on the day.
Among stocks, Agilent Technologies dropped 7.0 percent after posting a disappointing quarterly forecast late on Monday.
Ford dipped 0.9 percent after Piper Jaffray cut its rating to "neutral" on the automaker's shares.
Symantec rose 3.0 percent after the anti-virus maker's bullish 2020 forecast eased concerns over the impact of an internal accounting probe. (Reporting by Medha Singh in Bengaluru Editing by Saumyadeb Chakrabarty)