Israeli President Reuven Rivlin tapped Prime Minister Benjamin Netanyahu to form the next government, setting off weeks of political jockeying as the incumbent tries to maintain his hold on power.

Mr. Rivlin’s announcement came as talks between Mr. Netanyahu and rival Benny Gantz to form a broad unity government after last week’s inconclusive election have failed to make progress. The president met again with Messrs. Gantz and Netanyahu on Wednesday to try to pressure them into reaching a power-sharing pact.

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