Top Democrats in the Massachusetts House unveiled a $63 billion state budget plan for the coming fiscal year, spending slightly less than Gov. Maura Healey’s plan while adopting her plans to save on health care costs.

The House’s spending bill would increase state spending by nearly 4%. It clocks in at about $33 million (five-one hundredths of a percent) lower thanwhat Healey filed in January, though its bottom line will likely grow when representatives add spending during debate later this month.

Like Healey, the House is not proposing to raise taxes to support state spending.

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“This budget will allow the commonwealth’s economy to continue to grow responsibly and remain competitive amid serious economic and political uncertainty,” House Ways and Means Committee Chair Aaron Michlewitz said.

Budget-writers in the Healey administration as well as the Legislature have flagged health care costs as among the greatest challenges this year as they grapple with federal changes including funding cuts and tighter eligibility rules for Medicaid.

Healey’s budget proposed a number of cost-control changes to curb what her team described as otherwise unsustainable spending growth at MassHealth, the state’s Medicaid program. Among other measures, Healey wants to eliminate MassHealth coverage of GLP-1 drugs for weight loss and to cap adult dental benefits at $1,000 per year.

The House, in its budget, is proposing a higher annual dental benefits cap of $1,750 and staying out of the way of the cut to weight-loss drug coverage. Healey is proposing the GLP-1 changes administratively, in a way that doesn’t require explicit authorization in the budget.

Michelwitz said the House budget “doesn’t touch” the question of GLP-1 coverage at MassHealth, but that he anticipates lawmakers will “have a further conversation” on the issue in the future.

Speaker Ron Mariano said the House is adopting Healey’s cost controls to “help constrain the MassHealth budget as we work to navigate federal cuts and protect Massachusetts residents who rely on that coverage.”

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In a divergence from Healey, the House budget would steer a portion of the state’s sports-betting revenue to a fund that will support major sports and entertainment events in Massachusetts. Healey proposed putting the same 7.5% of sports gaming money into an economic development trust fund.

Michlewitz said that money would be for future events and would not be available for the FIFA World Cup matches happening this summer in Foxborough.

“I think the idea here is to show that we are open for folks that want to bring those types of events here to Massachusetts,” he said. “They’re great revenue sources, they’re great job opportunities for folks here in Massachusetts. We want those types of events to come here.”

House leaders want to spend nearly $10 billion in local aid to cities and towns. The bulk of that money would go to school districts, while $1.3 billion is for flexible aid to local governments.

That flexible aid money is not restricted to any one purpose and is a key component of most municipal budgets. As cities and towns across the state struggle to fund services amid rising costs, the Massachusetts Municipal Association had asked for a major boost to that account this year.

While the association requested a 26% increase in unrestricted local aid to help bring cities and towns back from what it called a “fiscal breaking point,” the House budget goes for an increase of less than 1%.

Michlewitz, in presenting the spending plan, emphasized the total local aid figure of nearly $10 billion, calling it a “huge amount of money in our budget.” He told reporters later that the MMA’s ask of a 26% increase was “unrealistic.”

He said the House budget raises total local aid by more than 5%, “above the average of what the rest of the budget is seeing in increases.”

“We understand budgets are tough,” said Michelwitz, a Democrat from Boston’s North End. “We’re having difficult times doing our budget too, so we certainly sympathize with them, but we know that the state is producing here.”

To address a specific financial challenge some cities have flagged, the House wants to set aside $10 million to help school districts that have experienced “unexpected enrollment reductions” among students who are not native English speakers.

In communities with large immigrant populations, school leaders say they’ve seen student populations drop amid fear of immigration raids, and with some families being deported or voluntarily returning to their home countries. Because school funding is tied to the number of students in a district, educators and advocates in communities including Framingham and Chelsea have asked lawmakers for extra money this year to help them avoid budget cuts.

House lawmakers will debate their version of the budget in late April, and the Senate will write and debate its own plan in May.

The two chambers will then negotiate with the goal of having a final budget in place by the time the new fiscal year starts on July 1, a deadline Massachusetts routinely misses.