WASHINGTON—The Rev. Jesse Jackson and his oldest son, former Rep. Jesse Jackson Jr. (D., Ill.), have urged President Trump to pardon Rod Blagojevich, the former Illinois governor whose arrest on charges of trying to sell a Senate seat ensnared the younger Mr. Jackson.

“We stand with his family as they seek a full pardon for a father and husband that has served most of a sentence that was far longer than the offense deserved,” the two said in a letter to the president dated last Friday. Mr. Blagojevich, a Democrat who served…