WASHINGTON—Utah Sen. Orrin Hatch said on Tuesday he would retire when his current term ends next year, opening the door for a possible political comeback by 2012 Republican presidential nominee Mitt Romney.

Mr. Hatch, 83 years old and the longest-serving Republican senator, had been urged by President Donald Trump to run for re-election to an eighth term in 2018. But voters and political forces in Utah, including the state’s largest newspaper, have pressed him to retire.

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