BRIDGEWATER, N.J.—President Donald Trump pledged a tougher law enforcement response to an epidemic of opioid addiction, and top officials in his administration said they wanted to increase the availability of an anti-overdose treatment in response to the crisis.

“Nobody is safe from this epidemic that threatens all—young and old, rich and poor, urban and rural communities. Everybody is threatened,” Mr. Trump said on Tuesday from the clubhouse at Trump National Golf Club in Bedminster, N.J., where he is spending a working vacation.

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