WASHINGTON—House Democrats said they would explore allegations President Trump has sought to limit documentation of his meetings with Russian President Vladimir Putin.

House Foreign Affairs Committee Chairman Eliot Engel (D., N.Y.), responding to a Washington Post report about Mr. Trump’s meetings with the Russian leader, said his committee would hold hearings on the claims, in what could be one of the first actions by Democrats to probe the president since they took control of the House in January.

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