There could be a new hurdle in the saga to redevelop the defunct Winthrop Square Garage: The 750-foot skyscraper planned for the site would cast long shadows over Boston Common and the Public Garden.

And the shadows would violate state laws.

The tower Millennium Partners wants to put up would extend shadows for as long as 90 minutes in the morning over the beloved parks, perhaps reaching the start of the Commonwealth Avenue Mall, a mile away, at certain times of year.

To move the billion-dollar project forward, the Walsh administration wants to tweak quarter-century-old statutes governing shadows cast over the two parks. But parks advocates and some key lawmakers are concerned, saying a change in the law could encourage construction of more towers darkening the two historic public spaces.

“It’s not just about one building,’’ said Liz Vizza, executive director of Friends of the Public Garden. “This is one building, but there’s going to be another building and another building after that.’’

At issue is a pair of state laws passed in the early 1990s that bar new construction in most of downtown Boston and the Back Bay from casting any shadows on the Common and Garden for more than one hour a day. They emerged from a successful battle neighborhood residents pitched against a skyscraper at Park Plaza in the 1970s.

While more modeling of its project needs to be done, Millennium concedes it will need relief from the laws.

“There’s no getting around that,’’ said state Representative Byron Rushing, who was briefed by Millennium last week.

Rushing has pushed, unsuccessfully, to expand shadow laws to protect Copley Place and other civic landmarks. “I’d rather not have any new shadow,’’ he said.

But city officials, who are selling the site to Millennium for $153 million, are aiming to allow at least a little more shade. In an agreement with Millennium set to be approved Tuesday, they pledge to seek special legislation to change the 26-year-old laws. To do so they’ll need a vote by the City Council and approval on Beacon Hill.

Details of what, exactly, they would propose are still being thought out, said Sara Myerson, chief of planning at the Boston Planning and Redevelopment Agency. But city officials say the plan would be a narrow expansion, designed for this project.

“It’s really a question of how much they need, which is still in development,’’ Myerson said last week. “We’re trying to work through the details.’’

City officials point out that any of the six proposals they received this year for Winthrop Square would have cast shadows on the Common. Indeed, development experts say any building of more than about 400 feet on the site, which is due east of the Common, would likely violate existing law. While buildings close to Boston Common, such as the new Millennium Tower on Washington Street, have a bit more leeway, there hasn’t been a tower tall enough to test the rules elsewhere in the Financial District since the law took effect in 1990.

That has some lawmakers wondering if a broader look at the shadow regulations might be in order.

“I’m not particularly interested in supporting a one-off exception to the shadow laws,’’ said Michelle Wu, president of the City Council. “I’d hope this would be in the context of a larger conversation around planning and development and how it impacts shared enjoyment of a great public asset like the Common.’’

State Representative Aaron Michlewitz, whose district includes much of the Financial District, said he too wants to take a careful look at details before lending his support. The shadow laws have worked well for 26 years, he said. They shouldn’t change lightly.

“I worry about opening up a can of worms here,’’ he said.

Still, the city has a lot riding on Winthrop Square. Millennium is agreeing to pay $153 million to buy the condemned garage and build a 55-story tower of condos and office space. It will pay $10 million up front, money the city is agreeing to give back if it can’t get the shadow laws rewritten. And at a height low enough to cast no shadow — perhaps 400 feet instead of 750 — the project may not be financially feasible, development experts say.

Joe Larkin, who is spearheading the project for Millennium, and Boston Planning and Redevelopment Agency officials said details of the tower’s silhouette will likely change as it moves through design review. That in turn could impact its shadow. But there will certainly be some new shade in the morning, Larkin said, which means it is up to the city to decide what it values more: the tower, or no new shadows on the Common.

“That’s not for me to decide,’’ Larkin said. “It’s a change in the law. So that’s for public officials and the community to decide, and we hope they agree.’’

Tim Logan can be reached at tim.logan@globe.com.