U.S. stocks staged a broad afternoon rally to gain ground Friday, but the S&P 500 still logged its largest weekly drop of 2019 following a volatile stretch dominated by U.S.-China trade policy updates.

Stocks slid to start the day, sending the Dow Jones Industrial Average down nearly 360 points, before rebounding in the afternoon. The rally came after Treasury Secretary Steven Mnuchintold CNBC the most recent trade talks were “constructive” and President Trump tweeted that tariffs “may or may not be removed” depending on...