Stocks posted their biggest drop in months Monday after officials in Beijing and the White House exchanged fresh threats in a trade fight that many observers fear could crimp growth.

The Dow Jones Industrial Average fell 617.38 points, or 2.4%, to 25324.99 and the S&P 500 dropped 69.53 points, or 2.4%, to 2811.87, with both indexes posting their biggest one-day losses since Jan. 3. The Nasdaq Composite declined 269.92 points, or 3.4%, to 7647.02 in its worst showing since December.

The...