"In time," he said.
From the back of the room, Cagle aide Brian Robinson jumped in: "Now's a good time."
Williams, seeming flustered, was peppered with several more questions about backing up his claims, each time saying he would not do so.
"We have a very long race ahead of us," he said.
Williams is centering his campaign on his loyalty to Donald Trump - he was the first state elected official in Georgia to endorse him - and he's tried to steal a page from his playbook with one headline-grabbing accusation after another.
Williams also made a string of blunders, including a much-distributed picture he took in June with a controversial militia and a rocky interview with CNN where he struggled to answer questions on the GOP healthcare bill.
Though he's run an in-your-face campaign, he's no fringe candidate. He's twice been elected to a state Senate seat in deep-red Forsyth County, and he's already pumped $1 million of his own fortune into the campaign to bolster the paltry $50,000 he's raised.
The event on Thursday touched on an early flash-point in the governor's race. Cagle said last week he was exploring the idea of setting a new minimum wage for police officers, months after Williams pushed a similar proposal that failed to gain traction.
But the circus-like spectacle of the event - Cagle staffers briefly considering hiring clowns to interrupt the press conference - evoked memories of the last time a GOP candidate for governor advertised a "major" press conference outside his top rival's office.
Former Dalton Mayor David Pennington's 2014 event, just a few feet from Gov. Nathan Deal's second-floor statehouse digs, featured a hand-lettered sign, snickering Deal staffers and a made-for-TV interruption from the governor's attorney - who ended up speaking longer than Pennington.
Thursday's event delivered a similar scene: A small group of reporters flanked by a wider ring of Capitol staffers and campaign deputies curious about Williams' threat to unleash Cagle's "previously undisclosed actions."
After the event, as Williams quickly disappeared and head-shaking staffers returned to their offices, state Sen. Renee Unterman stayed behind. In unsparing terms, she accused Williams of running a "fraudulent" campaign and of playing bait-and-switch with overhyped promises.
"He wants to lead the voters on and the media on," said Unterman, who backs Cagle. "It's fluff. And it's not very good fluff."