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Boston lawmakers on Monday amplified their concerns about the potential for the city to host the 2024 Olympic Games, saying they were concerned the infrastructure costs to the state would top $5 billion, as Beacon Hill struggles to get a handle on a process many officials fear has slipped from their grasp.

After meeting with opponents of the proposal, several members of the Boston delegation said they expected the Legislature to ratchet up its involvement in the planning for the games.

“After today, I think you are going to be hearing more from the Legislature,” said state Representative Michael J. Moran, a Brighton Democrat and one of Speaker Robert DeLeo’s top deputies.

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“It’s something we all should be concerned about from the state level,” Moran said of the prospective impact on state finances, calling the meeting “eye-opening, in some respect.”

Olympic bid organizers have said that transportation infrastructure spending would go toward previously planned projects.

“It’s unfortunate that the opponents are misleading the public by including billions of dollars in transportation funding that will be spent regardless of whether Boston hosts the 2024 Games,” Boston 2024 executive vice president Erin Murphy Rafferty said in an e-mail. “We have been very clear that the operation of the Games will be paid for with revenue from the Games and private funds.”

But both Moran and state Representative Aaron Michlewitz, a North End Democrat also close to DeLeo, said they were concerned that state coffers would be tapped without sufficient input from lawmakers, and that questions remain about how much.

“It’s pretty clear that, whatever it is, it’s going to be a significant chunk of change coming from the Commonwealth, and that’s something we’re going to have to delve into,” Michlewitz said.

Mayor Martin J. Walsh of Boston has been a vocal proponent of the Olympic effort. Moran and Michlewitz helped draft one of Walsh’s opponents during the 2013 mayoral campaign, Charlotte Golar Ritchie, who placed third, and have opposed him on some legislative policies.

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A muscular assertion of legislative prerogative could prove troublesome for the pro-Olympic forces, who have sought to ward off the impression that a well-organized resistance movement could hobble the bid to host the Games. Last week, for instance, then-Boston 2024 chief executive Dan O’Connell, who stepped down Friday, said the group opposed a referendum, but downplayed the negative impact a vote of disapproval could have on the proposal.

In bidding documents submitted to the US Olympic Committee, and made public last week, Boston 2024 played up support from major political players and said it “could envision proposal of comprehensive Olympic legislation to facilitate venues and transportation in a unified manner.”

Monday’s session provided the latest, and perhaps loudest, reminder from state officials that — with the Olympic organizers planning on state money, new laws, and the creation of a new public agency — the road to Boston 2024 runs through Beacon Hill.

Both DeLeo and Senate President Stanley C. Rosenberg, an Amherst Democrat, last week said they wanted Olympic events to stretch beyond Greater Boston, and several Boston lawmakers said they had heard from colleagues in other pockets of the state concerned that the capital would disproportionately benefit from Olympic spending.

“As a Boston rep, I’m elated that billions of dollars would be invested in my city,” said state Representative Jeffrey Sánchez, a Jamaica Plain Democrat who has served as a committee chairman under DeLeo. “At the same time, I’m a rep who works with 200 colleagues from across the Commonwealth, and I’d want to know what they say, as well.”

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Sánchez said he hoped the Olympics did not divert resources from what he called more pressing priorities.

“My Olympics are what’s happening in my community,” he said. “That has to do with the crime, the violence, and the education and the health care they’re receiving.”

A spokesman for the Olympic effort said the state’s $13.7 billion in expected transportation infrastructure spending over the next decade, authorized in 2013, should cover many costs.

“The concepts that we’ve put forward to the USOC and that we presented to the public last week are supported by projects that are in the transportation bond bill,” said Doug Rubin, spokesman for Boston 2024.

But critics have argued that those projects could come at the expense of others that have been waiting for funding far longer. And, Moran said, whether all of the Olympic infrastructure plans, some of which are not explicitly named in the 2013 bill, could be included under the bond bill was “a very gray area.”

Two members of the opposition group No Boston Olympics met with lawmakers for more than an hour in the House members lounge Monday. In a PowerPoint presentation, they outlined the $14.3 billion budget that Boston 2024 submitted to the USOC.

They also cited a University of Oxford study of the costs of every Games from 1960 to 2012, which found that the average cost overruns in real terms had been 179 percent.

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Jim O’Sullivan can be reached at jim.osullivan@globe.com. Follow him on Twitter at @JOSreports.