WASHINGTON—A congressional panel voted on Monday to make public a classified Republican-authored memo that alleges surveillance abuses against an associate of President Donald Trump dating back to the 2016 campaign.

The GOP-led House Intelligence Committee invoked an obscure rule in its effort to release the memo that was drawn from highly classified law-enforcement material and written under the direction of its chairman, Rep. Devin Nunes (R., Calif.), a close ally of Mr. Trump.

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