Washington (CNN) President Donald Trump called for the firing of Broward County Elections Supervisor Brenda Snipes and suggested without evidence that Republicans don't win elections "because of potentially illegal votes" during an interview on Wednesday.

"You look at her past, she's a disaster," Trump told the Daily Caller , referring to Snipes, adding, "I won Florida and, you remember? That area, Broward, didn't come in. ... You can only put in so many votes, although she may change that system."

He later added, "Oh, she should have been removed -- I think she should have been removed in the middle of this mix-up."

Snipes, a Democrat, has been the target of repeated and direct attacks from Republicans throughout the Sunshine State as Florida's Senate, governor and agriculture commissioner races are recounted following the midterm elections earlier this month.

Former Gov. Jeb Bush, who first appointed Snipes to the post, called for her to step down on Monday. Gov. Rick Scott, whose Senate race is central to the recount, sued her and has used her as a foil for days. And dozens of Trump supporters protested outside of Snipes' office in Broward County, some holding signs labeling her the "Supervisor of Corruption."

Snipes has kept a low profile through much of it, but even Democrats in Florida admit the criticism is not entirely without reason: Broward County's elections office has been hampered by controversies for years and Snipes has been plagued by questions of bias for much of her tenure.

Snipes hinted Tuesday that she may not be in the job very long, saying it was "hard to rule out race" as a factor in the criticism being lobbed at her.

"It is time to move on, to let someone else" do the job, Snipes said. When a reporter followed on whether she will step down, the election official backed off slightly.

"Well, I haven't finalized that. I'll just check with my family. They'll tell me what I'm doing," she said.

In his interview on Wednesday, the President also suggested, without evidence, that voter fraud was taking place.

"The Republicans don't win and that's because of potentially illegal votes," Trump said. "When people get in line that have absolutely no right to vote and they go around in circles. Sometimes they go to their car, put on a different hat, put on a different shirt, come in and vote again. Nobody takes anything. It's really a disgrace what's going on."

There have been no reports of the kind of fraud the President described.

"If you buy a box of cereal -- you have a voter ID," Trump continued, appearing to reference his previous argument that identification is required for buying groceries. There is no such requirement except for purchases of alcohol and cigarettes.

"They try to shame everybody by calling them racist, or calling them something, anything they can think of, when you say you want voter ID. But voter ID is a very important thing," he continued.

The President has repeatedly warned against "illegal voting" during his tenure in office, dredging up a familiar trope he popularized during the 2016 presidential election. There is well-established evidence that voter fraud is extremely rare

For example, stealing someone's identity to vote is less likely than being struck by lightning, as the nonpartisan Brennan Center for Justice at the New York University School of Law put it.