TEL AVIV—Buoyed by a resounding victory in a party leadership election, Israeli Prime Minister Benjamin Netanyahu brandished his close ties with President Trump to woo right-wing voters as he attempts to break a monthslong political deadlock in the country.

Mr. Netanyahu defeated Likud rival Gideon Saar in Thursday’s primary contest, winning nearly three-quarters of the votes despite corruption charges against him, to lead the party in March’s national election. He failed to form a ruling coalition after inconclusive votes…

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