He has been trying to focus attention on Mr. DeSantis from the political left, attacking him for his votes on Medicare and Social Security while he was a congressman and trying to paint him as an establishment figure.
To that end, Mr. Trump’s allies didn’t plan to let Mr. DeSantis have a quiet rollout of his book. A group called Villagers for Trump sought Trump supporters to attend a late-afternoon event that Mr. DeSantis was holding on Tuesday in the community known as The Villages.
The “Trump Train,” a group of roughly 10 fervent Trump supporters, heeded the call.
But almost as soon as the supporters — who included Laura Loomer, a far-right activist and conspiracy theorist — pulled out their signs and began to protest in the parking lot, they were shut down by security, as well as the local police and the shopping center property manager.
Rick Carlins, 71, a retiree who lives nearby in Fruitland Park, said he was frustrated with Mr. DeSantis, after Mr. Trump has supported his political career. “I couldn’t, as a person, run against someone who tried to get me in office,” Mr. Carlins said as he walked away from the parking lot.
The attacks on Mr. DeSantis from Trump allies are expected to intensify, as Mr. DeSantis’s advisers have signaled he won’t declare a candidacy until after the Florida legislative session ends. That gives Mr. Trump a specific window in which to try to define Mr. DeSantis with Republican voters — and general election voters — before Mr. DeSantis has a chance to do so as a candidate.
Mr. Trump is expected to have a well-funded super PAC. But Mr. Trump is not expected to have is a large portfolio of wealthy donors supporting him. Many have lined up behind Mr. DeSantis, investing in his 2022 re-election as a way of getting involved ahead of a formal campaign.
Last weekend, Mr. DeSantis held a donor retreat with a number of people who are likely to be part of a campaign, as well as some who are not.
Some senators and governors attended, as Mr. DeSantis moderated panels. That included one on election integrity, during which Mr. DeSantis told the crowd that Republicans needed to be engaged with mail-in voting, according to a person present.
Reid J. Epstein, Michael C. Bender, Neil Vigdor and Abigail Geiger contributed reporting.