WASHINGTON—Support is growing among Democrats to begin an impeachment inquiry into President Trump, a new Wall Street Journal/NBC News poll finds, presenting a challenge to House Speaker Nancy Pelosi, who has so far opposed hearings as politically costly and divisive.

The share of Americans in the survey calling for immediate impeachment hearings jumped 10 points, to 27%, since last month. The share of those who believe Congress should avoid hearings and allow Mr. Trump to finish his term stood at 48%, unchanged since May.

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