"We must defeat Trump. He has failed us at every turn," the 77-year-old added.
Bloomberg's personal appearance to sign his ballot papers in Little Rock is a strong public signal that the centrist tycoon will officially leap into the already-crowded Democratic primary field.
"Mike wanted to go and do the filing himself" in Arkansas, Bloomberg spokesman Jason Schechter told The New York Times.
"If he runs, he's going to go to states that Democrats never go to in the primary campaign. We're starting that today in Arkansas." Bloomberg, who like Trump is a septuagenarian white New York billionaire, said back in March that he wouldn't run, but more recently has been toying with the idea of throwing his hat in the ring, according to an advisor.
He has changed his political affiliation on multiple occasions, including switching from Democrat to Republican when he successfully ran for mayor of New York in 2001. He became an independent six years later.
Bloomberg is believed to be concerned that the Democratic Party has shifted too far left in recent years, and that a progressive nominee like senators Bernie Sanders or Elizabeth Warren would lead to Trump's re-election.
Experts say a Bloomberg candidacy could hurt the current frontrunner Joe Biden, the former vice president who is the leading centrist in the race.
Trump last week predicted that Bloomberg would "hurt Biden" if he ran, saying "there's nobody I'd rather run against than Little Michael.
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