As President Donald Trump drew criticism from several top Republicans for his pardon of former Sheriff Joseph Arpaio, the Arizona lawman said Republican lawmakers should rally behind a president who he said would be counted among the greatest in history.

“They’re trying to go after the president. He’s a great guy and I’m with him and will always be with him,” said Mr. Arpaio, a longtime sheriff in Maricopa County, Arizona, in an interview Sunday. “I’m sad what they’re doing to him. It’s sad.”

Several...