Businesses in Massachusetts are demanding an end to the program that fined them more than $300 million in 2018 for failing to provide health coverage for their workers.

The Associated Industries of Massachusetts, a group representing 4,000 businesses, plans to file legislation by Jan. 18 that would end the fines, Christopher Geehern, executive vice president of AIM, told Bloomberg Law.

Gov. Charlie Baker (R) advocated the fines of $750 per uninsured employee to bolster Medicaid, the federal-state program that provides health coverage for the poor. The fines are levied by the state Department of Revenue on businesses with six or...