Mr. Cain, 74, had recently been undergoing oxygen treatment after being hospitalized for the coronavirus in early July.
“There aren’t many people like Herman Cain, and it behooves us to truly cherish the ones we’re given,” Dan Calabrese, the editor of hermancain.com, wrote on Thursday. “His wife Gloria — his children Melanie and Vincent — and his grandchildren … they need our love, our support and our prayers.”
“I’m sorry I had to bring you bad news this morning,” Mr. Calabrese said. “But the good news is that we had a man so good, so solid, so full of love and faith … that his death hits us this hard. Thank God for a man like that.”
Mr. Cain attended President Trump’s June 20 rally in Tulsa, Oklahoma, though Mr. Calabrese had previously said they had no idea how he contracted the virus.
White House press secretary Kayleigh McEnany said Mr. Cain “embodied the American Dream and represented the very best of the American spirit.”
“Our hearts grieve for his loved ones, and they will remain in our prayers at this time,” she said on Twitter. “We will never forget his legacy of grace, patriotism, and faith.”
Mr. Cain, a cancer survivor and the former CEO of Godfather’s Pizza, received news on June 29 that he tested positive for the coronavirus and he was hospitalized in early July.
His team had said earlier this week he was still in the hospital being treated with oxygen but appeared to be getting better.
Mr. Trump said Thursday that he spoke to Mr. Cain’s wife and children to express his “deepest condolences,” calling him a “great man.”
“My friend Herman Cain, a Powerful Voice of Freedom and all that is good, passed away this morning,” Mr. Trump said on Twitter. “Herman had an incredible career and was adored by everyone that ever met him, especially me. He was a very special man, an American Patriot, and great friend.”
Earlier in the day, Ellen Carmichael, a Republican strategist and former spokeswoman for Mr. Cain’s presidential campaign, tried to preempt ghoulish commentary on his death.
“I’m very saddened to learn of the passing of my former boss, Herman Cain,” Ms. Carmichael said on Twitter. “I’m bracing for the cruelty online about how he deserved to get COVID and die because of his politics. We’re living in a dark time. But, they didn’t know him. I did.”
He ultimately bowed out of the race in December 2011 amid sexual misconduct allegations, which he denied.
• Dave Boyer contributed to this story.
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