Mueller convened a grand jury as part of his investigation into Russian interference in the 2016 election as well as any possible connections between Russia and Trump campaign associates.
The sweeping indictment describes an unprecedented campaign by Russia to influence the election, affirming the longstanding conclusions of the US intelligence community.
It is at odds with Trump's repeated questioning of those conclusions.
Trump has said that despite the charges, the Russian meddling had no effect on the outcome of the election. In a separate tweet late Saturday, he said "the only collusion was between" Russia and Hillary Clinton.
The FBI has acknowledged receiving two tips that appear to relate to Cruz ahead of the shooting. One was a January 5 call to a tip line from someone close to him -- one that the FBI said it failed to act on.
The caller provided information about "Cruz's gun ownership, desire to kill people, erratic behavior, and disturbing social media posts, as well as the potential of him conducting a school shooting," the bureau said.
The information should have been assessed as a "potential threat to life," but the proper protocols weren't followed and the FBI's Miami office was not notified, the agency said.
FBI Director Christopher Wray said the bureau is investigating what happened.
"We have spoken with victims and families, and deeply regret the additional pain this causes all those affected by this horrific tragedy," Wray said in a statement.
The FBI's admission prompted Florida Gov. Rick Scott to call on Wray to resign.
In addition to the call, a video blogger said he warned the FBI in September about a possible school shooting threat from a YouTube user with the same name as Cruz.
An FBI agent confirmed a field officer in Jackson, Mississippi, received the tip and interviewed the person who shared it.
But no additional information was found to help identify the person who posted the comment and no connection was made to South Florida, said FBI special agent Robert Lasky, who is in charge of the Miami division.
The FBI's missteps have raised questions about whether it could have prevented the shooting. Attorney General Jeff Sessions ordered a review Friday into how the Justice Department and FBI respond to indications of potential violence.
"We will make this a top priority," Sessions said in a statement. "It has never been more important to encourage every person in every community to spot the warning signs and alert law enforcement. Do not assume someone else will step up -- all of us must be vigilant. Our children's lives depend on it."
Sen. Marco Rubio, R-Florida, also called for the House and Senate to conduct investigations into how the FBI reviews public tips in similar instances.