"The Department of Justice, when it comes to law enforcement, is independent," White House press secretary Karine Jean-Pierre said. "This is what we believe."
Law enforcement has been concerned about classified material at Mar-a-Lago that Trump took with him when he left office.
Trump posted the request hours after the Justice Department asked a court to unseal the warrant.
"Garland is playing chess. Donald can only play checkers," Donald Trump's niece said.
Attorney General Merrick Garland said he personally approved the decision for the FBI to seek a search warrant for Trump's residence.
The Department of Justice has moved to unseal the warrant used in the raid on Donald Trump's Florida home.
Monday's raid marked a dramatic escalation of law enforcement scrutiny of Trump, who faces an array of inquiries tied to his conduct in the waning days of his administration.
Officers were accused of using false information to obtain the search warrant that led to Taylor's killing.
The Justice Department has faced criticism over its handling of the plot to overturn the 2020 presidential election.
The Justice Department says a Russian operative has been charged with using political groups in the United States to advance pro-Russia propaganda.