Governor Charlie Baker’s push to compel businesses to cover more of the state’s ever-rising health care costs gained momentum Tuesday after his administration scaled back a controversial plan that had angered business leaders.

Administration officials asked lawmakers to allow an increase to an existing fee on employers to raise an estimated $200 million annually for health coverage. The request comes just 10 days before the start of the next fiscal year, as House and Senate members are hashing out a new budget amid a revenue shortfall.

Baker had initially proposed raising $300 million in the next fiscal year through a fee that would have charged many businesses $2,000 per worker to help pay the costs of the state Medicaid program, called MassHealth. After a backlash and many subsequent meetings with employer groups, administration officials said Tuesday that they now have a plan that enjoys the business community’s support.

Baker’s new approach gives ground in several key areas. For one, the additional assessment would end after two years. Baker’s original plan to charge businesses had no planned end date.

The new proposal uses an existing assessment that almost all businesses already pay, called the employer medical assistance contribution, or EMAC, to raise money. This contribution would increase from $51 to $77 per employee.

But employers whose workers currently receive public health benefits would pay as much as $750 more per worker.

The new fee would raise an estimated $200 million in the next fiscal year.

In another sweetener for the business community, the administration proposed changing unemployment insurance rates so employers would pay smaller increases for two years.

Several business groups said Tuesday that they no longer oppose the governor’s proposed fee. They said they appreciated the fact that the assessment would be temporary and more geared toward companies whose employees rely on MassHealth.

“We have to look at it from where we started in January,’’ said Jon Hurst, president of the Retailers Association of Massachusetts. “Compared to what was first rolled out, it is so much better.’’

But not everyone was ready to praise the administration’s plan. The Greater Boston Chamber of Commerce, one of the most vocal groups on this issue, declined to comment, and the Chamber was missing from a list pro-business sound bites distributed by the administration.

Lora Pellegrini, president of the Massachusetts Association of Health Plans, called the administration’s new proposals “on the whole . . . a positive development.’’

“By working with the business community, they found a place of compromise,’’ Pellegrini said. “They’ve also come up with strategies to reduce the cost of enrollment in MassHealth and put some market-based solutions in place for the commercial market.’’

Administration officials called for a series of changes to MassHealth — including toughening eligibility rules and covering fewer prescription drugs — that they project will save the state another $115 million per year. MassHealth, which is jointly funded by the state and federal governments, provides coverage to about 1.9 million Massachusetts residents, including the poor and people with disabilities.

Following a strategy used by commercial insurers, the administration wants to limit the number of similar drugs MassHealth covers for a particular condition. For example, if there are four drugs available to treat a certain condition, officials might only pay for the two most cost-effective ones.

Baker’s finance secretary, Kristen Lepore, asked the House and Senate budget chiefs to include the administration’s proposals in the spending plan they are finalizing for the fiscal year that begins July 1.

“While our administration has made it a priority to control spending at MassHealth and has slowed its growth rate over the past two years, further action must be taken to contain the program’s growth,’’ Lepore said in a letter to Senator Karen E. Spilka and Representative Brian S. Dempsey.

Through their spokespeople, Spilka and Dempsey did not comment Tuesday other than to say they were still reviewing the administration’s latest proposal.

House and Senate leaders previously said they supported raising about $180 million from businesses to help pay for MassHealth, but they left the details up to the Baker administration. At about $16 billion annually, MassHealth is the single biggest piece of state spending.

Missing from the administration’s latest list of proposals was a cap on payments to high-priced hospitals. The governor suggested price caps as a way to curb health care costs in his earlier budget proposal, but House and Senate leaders nixed that idea. The hospital industry lobbied against price caps.

Lynn Nicholas, president of the Massachusetts Health & Hospital Association, said in a statement that the group “appreciates the Baker administration’s efforts to address the financial challenges facing the state while recognizing the . . . economic contributions of Massachusetts hospitals, health systems and other care providers.’’

The administration’s proposals for tackling health care spending include a five-year moratorium on new health insurance mandates, which insurers and small businesses often blame for driving up costs.

The administration also wants to restore a rule that stopped residents with access to “affordable’’ health insurance through employers from enrolling in MassHealth. And they want to move 140,000 adults now on MassHealth into subsidized commercial plans on the state Health Connector. These changes require federal approval, which the administration plans to request this summer. They also need approval from the state Legislature.

Already, the administration is restructuring MassHealth to move to a model of “accountable care,’’ which aims to control costs and better manage patients’ health by keeping them within set networks of providers.

Employer groups said they appreciated the steps taken by the administration to curb the escalating costs of health coverage for poor and low-income residents.

“Now it feels like the package has some connection to the problem, which is the unsustainable cost of Medicaid,’’ said JD Chesloff, executive director of the Massachusetts Business Roundtable.

Eileen McAnneny, president of the business-backed Massachusetts Taxpayers Foundation, said she supports the administration’s latest proposal largely because it’s a step toward addressing the biggest cause of the state’s budget pressures.

“There are lots of priorities in state government [and] providing health insurance to people is certainly an important one,’’ said Mark Gallagher, executive vice president at the Massachusetts High Technology Council. “As a program starts to creep up to 40 percent of the state budget, it starts to become the one and only priority of state government, and everything else is pushed far down the priority list.’’

Priyanka Dayal McCluskey can be reached at priyanka.mccluskey@globe.com. Follow her on Twitter @priyanka_dayal. Jon Chesto can be reached at jon.chesto@globe.com. Follow him on Twitter @jonchesto.