ROME—President Giorgio Napolitano, who led Italy through one of its stormiest political periods, resigned Wednesday, opening a phase of political uncertainty that will test the strength of Prime Minister Matteo Renzi’s young government.

Mr. Napolitano, who turns 90 in June, announced in December that he had decided to end his second mandate ahead of time due to his age and increasing “signs of fatigue,” which made it increasingly difficult for him to fulfill his duties.

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