Boston Mayor Michelle Wu doubled down on refuting her opponent Josh Kraft’s claim that the city’s White Stadium pro soccer rehab could cost taxpayers $172 million as “entirely false,” but wouldn’t provide an updated cost estimate.

Wu said Thursday that the internal city document that Kraft revealed earlier this week and included a $172 million budget for the city’s half of the public-private project — nearly double what her administration projected last December — was leaked inappropriately to her opponent’s campaign for “political purposes.”

“The assertion that there’s this secret, fake, very high number floating around, it’s entirely false,” Wu told reporters after an unrelated event in Roxbury.

Wu rehashed what she said earlier this week about the document representing a “contingency” budget for the White Stadium project, half of which will be paid by taxpayers with the other half covered by Boston Unity Soccer Partners, a for-profit group that owns the city’s National Women’s Soccer League expansion team.

The new professional women’s team, Boston Legacy FC, is under a 10-year lease agreement with the city to share use of White Stadium with Boston Public Schools student-athletes. Critics of the public-private project, including Kraft, say they would rather see a high-school-only rehab of Franklin Park’s White Stadium.

On a Tuesday radio program, Wu called the $172 million figure a “worst-case scenario” based on a “disaster planning” budget compiled by the city’s public facilities department.

She was responding to remarks Kraft made Monday outside White Stadium, where he blasted the ballooning cost of the controversial project, which has grown from the city’s initial budget of $10.5 million two years ago, to $50 million for the majority of last year, and then $91 million at the end of 2024.

“This is a catastrophic failure of city management,” Kraft said at the time.

Wu on Thursday described the initial budget of $10.5 million as a placeholder that was included in the city’s capital plan, which she said is typical of capital projects.

She further stated that the budget grew to $91 million based on design changes that were incorporated based on community feedback.

Wu declined to provide an updated cost estimate, saying that the city would have a clearer sense of updated costs after different aspects of construction go out to bid in the “next couple of weeks.”

She mentioned earlier this week that the cost was likely to increase due to federal tariffs that have led to higher steel prices, escalating construction costs driven by “uncertainty in the economy,” and additional design changes.

Kraft countered Wednesday by saying that he saw the city as already being in a “worst case scenario,” as Wu described the $172 million figure, “given what Trump and his disastrous tariffs are doing to the cost of steel and construction.”

“How much is going to be too much for the taxpayers of Boston, and don’t they deserve to know?” Kraft said.

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Wu on Thursday continued to dismiss the $172 million figure as inaccurate, but described the plan’s cost hikes as typical of the city’s capital project process.

“The budget department’s job is to create … some scenarios that the team can plan or discuss around,” Wu said. “That particular document that was accessed and then shared to a campaign for political purposes was not even part of any group discussion that was made.

“It hasn’t been part of the planning team or the project management team. It was a document that existed on someone’s hard drive and seems to have been accessed by a person who wasn’t affiliated with the project and probably didn’t understand it at all.”

When asked if a false number was leaked inappropriately, the mayor said, “Yes.”