* S&P 500 inches up in early trading
* Trump tweets on lack of progress in Mexico talks
* Mexican peso hit by Fitch downgrade (Updates with early U.S. markets activity, changes dateline; previous LONDON)
By Caroline Valetkevitch
NEW YORK, June 6 (Reuters) - The U.S. Treasury yield curve flattened on Thursday as the European Central Bank committed to leaving interest rates steady into the first half of 2020, while major world stock indexes were mixed following U.S. President Donald Trump's fresh tariff threat against China.
The ECB's move was less aggressive than what some traders had expected and led to selling in shorter-dated German government debt, which in turn spilled over into shorter U.S. Treasury maturities, traders and analysts said.
Much of the yield curve flattened, coming off its steepest level in seven months the previous day. The gap between two-year and 10-year yields narrowed by 2.6 basis points to 25.10 basis points.
German 10-year yields tumbled to a record low of -0.240% before retracing to -0.220%. Benchmark 10-year notes last rose 6/32 in price to yield 2.1036%, from 2.123% late on Wednesday.
U.S. stocks were mixed in early trading, with continued hopes of an interest rate cut from the Federal Reserve helping to support the market.
Adding to recent trade tensions, Trump said he would decide on more China tariffs "probably right after the G20," which followed his overnight threat to put tariffs on "at least" another $300 billion worth of Chinese goods.
"It feels like an escalation of tensions and may be an elongated trade war and we might have to recalibrate lower," said Art Hogan, chief market strategist at National Securities in New York.
The latest flare-up in tensions follows mixed economic data that rekindled woes over the health of the world's top economies but also spurred expectations that central banks could ride to the rescue.
The Dow Jones Industrial Average rose 91.85 points, or 0.36%, to 25,631.42, the S&P 500 gained 6.84 points, or 0.24%, to 2,832.99 and the Nasdaq Composite dropped 1.47 points, or 0.02%, to 7,574.00.
The pan-European STOXX 600 index lost 0.09% and MSCI's gauge of stocks across the globe gained 0.13%.
Mexico's peso suffered under a double whammy from trade woes with the United States and ratings agency Fitch downgrading the country's credit rating to BBB, while Moody's changed its outlook to negative from stable.
The Mexican peso lost 0.56% versus the U.S. dollar at 19.69.
The dollar index fell 0.4%, with the euro up 0.61% to $1.1287.
In the oil market, U.S. crude fell 0.29% to $51.53 per barrel.
Additional reporting by Richard Leong in New York; Medha Singh and Amy Caren Daniel in Bengaluru and Karin Strohecker in London; Editing by Sam Holmes, Toby Chopra and Dan Grebler