Legislation proposed Tuesday by Massachusetts Gov. Deval Patrick would eliminate a provision in the state's landmark health care reform law that imposes a fee on employers that do not offer coverage to their employees.

Under the governor's plan, the current annual assessment — known as the Fair Share contribution — of $295 per employee on employers not offering coverage would end on June 30.

In addition, a state program that now subsidizes coverage for eligible uninsured workers would be eliminated, as would a fee — currently $67.20 per employee — paid by employers to fund the program.

However, Gov. Patrick's proposal, which will require approval by state lawmakers, would require employees to pay a new fee of just over $50, which also would be used to finance the cost of subsidized care for low-income state residents.

A statement from Gov. Patrick's office said the $295 fee, established under the state's 2006 health reform law, should be eliminated because the federal health care reform law will make it unnecessary.

Under the Patient Protection and Affordable Care Act, employers with at least 50 employees will be liable, starting in 2014, for a $2,000-per-full-time-employee penalty if they do not offer coverage.

Without the elimination of the Fair Share assessment, “employers could be hit with double penalties if the two policies were to coexist,” according to the statement from Gov. Patrick's office.

While few big employers with employees in Massachusetts were liable for the penalty because nearly all offer coverage, they will welcome its elimination because of the burdensome filing requirements associated with the fee, consultants say.

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“The dropping of the Fair Share contribution requirement is great news for employers in eliminating a cumbersome annual filing requirement,” said Rich Stover, a principal with Buck Consultants L.L.C. in Secaucus, N.J.

State lobbyists say the proposal has an excellent change of passage, with no known opposition.

“I would say it has a very good chance of being passed,” said Bill Vernon, state director of the National Federation of Independent Business/Massachusetts in Boston.

In 2011, Massachusetts had the lowest uninsured rate — 3.4% — of any U.S. state, according to the U.S. Census Bureau.