President-elect Donald Trump spoke with Israeli Prime Minister Benjamin Netanyahu and Egyptian President Abdel Fattah Al Sisi on Wednesday and will have his first postelection meeting with President Barack Obama on Thursday to discuss the transfer of power between their two administrations in January.

Mr. Trump’s transition team has been gathering for months, and they packed into an office on Wednesday a block away from the White House to continue drafting blueprints for the new administration. Among the proposals: a policy...