WASHINGTON — Gov. Steven L. Beshear of Kentucky offered a vivid defense of his expansion of Medicaid under the Affordable Care Act on Friday, imploring Matt Bevin, the Republican governor-elect, to “look at this from a business standpoint, if not from a human standpoint,” and keep the program in place.

Mr. Bevin, a businessman who comfortably defeated Attorney General Jack Conway last week, frequently attacked the health law on the campaign trail. He initially vowed to reverse the state’s expansion of Medicaid, which has provided health coverage to an additional 425,000 low-income people, including many adults with no dependent children.

But more recently, Mr. Bevin has suggested he would seek federal permission to reshape the program, requiring participants to contribute to the cost of their coverage and possibly scaling back eligibility, something no state has received permission to do under the terms of the health law.

In a news conference in Frankfort, Mr. Beshear, a Democrat who is leaving office because of term limits, offered facts and figures to back up his argument that expanding Medicaid would save the state money and improve, as he put it, “our collective public image.”