Former Gov. Andrew M. Cuomo was denied more than $600,000 in public matching funds on Monday after the New York City Campaign Finance Board found that he likely engaged in illicit coordination with a super PAC supporting his campaign for mayor.

Mr. Cuomo first aroused suspicion when he posted on his campaign website what looked to be a set of detailed spending instructions for anyone hoping to help. The super PAC, Fix the City, began airing an ad just days later that appeared to align with some of those requests, echoing themes and data points.

The tactic in question, known as red-boxing, has become common in federal races as a way to circumvent anti-coordination rules. But the New York City campaign finance board has explicitly warned against it.

Mr. Cuomo still received $1.5 million in public matching funds, though he had theoretically qualified for $2.1 million. But the board decided to withhold $622,056 — the amount that the super PAC paid for the ad — because it said there was “reason to believe” that the television commercial was “not independent of the Cuomo campaign.”

Rich Azzopardi, a spokesman for Mr. Cuomo, said in a statement that the campaign would work to resolve the issue with the board.

“Our campaign has operated in full compliance with the campaign finance laws and rules, and everything on our website was reviewed and approved by our legal team in advance of publication,” he said, adding that other candidates had published similar information online. “We look forward to making that clear when we respond to the board’s preliminary ruling and receiving the full matching funds to which the campaign is entitled.”