The rapport between Barack Obama and Donald Trump is unraveling, with the president convinced that Mr. Obama is undermining his nascent administration and the former president furious over Trump tweets accusing him of illegal wiretapping, people close to the two men said.

The budding feud between two men who share the unique bond of membership in the commander-in-chiefs’ club is a fresh distraction in a Trump presidency that has been struggling to enact its agenda.

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