Trump has long accused it and the U.S. Justice Department of being out to get him.
Trump's closest rival for the nomination, Florida Governor Ron DeSantis, decried the "weaponization" of federal bureaucracy after Trump's indictment.
Haley said Trump had acted recklessly, although she also said the FBI and Justice Department had "lost all credibility with the American people."
None of the Republican president campaigns responded to requests for comment about their criticism of federal law enforcement and calls for an overhaul.
A spokesman for the Justice Department, which oversees the FBI, declined to comment.
Persons:
Donald Trump, Trump, Kyle Kondik, University of Virginia Center for Politics . Trump, Trump's, Hillary Clinton, James Comey, Clinton, Hunter Biden, Joe Biden, Biden, Christopher Wray, Timothy Naftali, Naftali, Ron DeSantis, Chris Christie, Asa Hutchinson, Nikki Haley, Haley, Bill Bowen, Bowen, Tim Reid, Nathan Layne, Gram Slattery, Ross Colvin, Alistair Bell
Organizations:
Republicans, Republican, Trump, U.S . Justice Department of, University of Virginia Center for Politics ., Reuters, White, FBI, Justice Department, Democratic, Department, New, South Carolina, Republican National Committee, U.S . Capitol, Thomson
Locations:
Russia, Florida, New Jersey, Arkansas, Portsmouth , New Hampshire