Florida Governor Rick Scott said the agency's director must resign, while Attorney General Jeff Sessions ordered a review, lamenting FBI "failures".
Some of those close to the 17 victims of Wednesday's shooting also voiced dismay at the FBI's actions.
President Donald Trump on Friday met survivors of the attack in Parkland.
Mr Trump and First Lady Melania Trump visited a hospital and later the local sheriff's office, thanking them for their response to the tragedy.
"What a great job you've done," Mr Trump told law enforcement officials, adding: "I hope you get credit for it because believe me, you deserve it."
Nikolas Cruz, 19, has confessed to carrying out Wednesday's attack at Marjory Stoneman Douglas High School in Parkland and has been charged with 17 counts of murder.
It was the deadliest US school shooting since 2012 and has re-ignited debates about gun control, with many students from the school weighing in.
It comes after the Federal Bureau of Investigation admitted it did not properly follow up on a warning about Mr Cruz.
On 5 January a person close to the suspect contacted the FBI tipline to provide "information about Cruz's gun ownership, desire to kill people, erratic behaviour, and disturbing social media posts, as well as the potential of him conducting a school shooting", an FBI statement said.
The FBI said that information should have been assessed as a potential threat to life and passed on to the Miami field office but that "we have determined these protocols were not followed".
FBI Director Christopher Wray said the bureau was "still investigating the facts".
"I am committed to getting to the bottom of what happened in this particular matter, as well as reviewing our processes for responding to information that we receive from the public," he said.
"We have spoken with victims and families, and deeply regret the additional pain this causes all those affected by this horrific tragedy," he added.
The 5 January tip was not the only information the FBI received about Nikolas Cruz.
In September, a Mississippi man reported to the law enforcement agency a disturbing comment left on a YouTube video by a user called "nikolas cruz" which said: "I'm going to be a professional school shooter."
Ben Bennight said he spoke to FBI representatives for about 20 minutes and that they contacted him again following the Parkland shooting.
The FBI on Thursday said they had conducted "checks" at the time, but were unable to identify the person behind the comment.
BBC
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