President Trump appeared to dare Howard Schultz to run for president after the former Starbucks CEO announced he's considering entering the fray as a "centrist" independent candidate. Mr. Trump tweeted Schultz doesn't have the "guts" to run for president, before — on a different note — saying he hopes Starbucks is still paying rent for the company's location in Trump Tower.

Schultz told CBS' "60 Minutes" in an interview broadcast Sunday that Americans are "looking for a better choice" than either party can offer.

"Howard Schultz doesn't have the 'guts' to run for President!" Mr. Trump said on Twitter Monday. "Watched him on @60Minutes last night and I agree with him that he is not the 'smartest person.' Besides, America already has that! I only hope that Starbucks is still paying me their rent in Trump Tower!"

Howard Schultz doesn’t have the “guts” to run for President! Watched him on @60Minutes last night and I agree with him that he is not the “smartest person.” Besides, America already has that! I only hope that Starbucks is still paying me their rent in Trump Tower! — Donald J. Trump (@realDonaldTrump) January 28, 2019

Some Democrats are urging Schultz not to run, believing he could siphon votes away from Democrats and give Mr. Trump a better shot at re-election, as CBSN's Caitlin Huey-Burns has reported.

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"I have a concern that, if he did run, that, essentially, it would provide Donald Trump with his best hope of getting re-elected," Julián Castro, another 2020 hopeful who served as secretary of Housing and Urban Development in the Obama administration, said on CNN's "State of the Union" Sunday. "I would suggest to Mr. Schultz to truly think about the negative impact that that might make."

But Schultz sees an opening.

"I want to see the American people win. I want to see America win," Schultz told "60 Minutes." "I don't care if you're a Democrat, independent, libertarian, Republican. Bring me your ideas. And I will be an independent person who will embrace those ideas. Because I am not, in any way, in bed with a party."

With the 2020 election cycle now in full swing, Mr. Trump hasn't hesitated to offer his opinions on the emerging candidates.

The president has particularly mocked Sen. Elizabeth Warren, whom he has repeatedly called "Pocahontas" in the past, for live-streaming her daily activities after announcing she's formed an exploratory committee.

"If Elizabeth Warren, often referred to by me as Pocahontas, did this commercial from Bighorn or Wounded Knee instead of her kitchen, with her husband dressed in full Indian garb, it would have been a smash!" Mr. Trump tweeted earlier this month.