DUBAI—Saudi Aramco said its first-quarter profit fell sharply and it would cut spending this year, underscoring the twin impact of an oil-price rout and the coronavirus pandemic on the kingdom’s worsening finances.

The Saudi Arabian Oil Co., as the state-controlled company is formally known, said Tuesday that net profit fell 25% to 62.5 billion riyals ($16.7 billion), from $22.2 billion in the first quarter a year earlier. Its revenue fell 16% to $60 billion.

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