DOVER — A task force is recommending lawmakers modify a program for first-time homebuyers by allowing the counties to place a cap on an exemption from the realty transfer tax.

Currently, an individual who is buying a first home in Delaware is exempt from a portion of the realty transfer tax. Purchase of any property triggers a 4 percent tax, evenly split between the seller and the buyer, except in the case of a person buying his or her first house.

All three counties have programs offering breaks to first-time buyers as part of an effort to encourage homeownership.

Kent exempts both the seller and buyer from its share of the tax — 1.5 percent — while both Sussex and New Castle require the seller to pay a 0.75 percent fee. All parties must still pay their half of the 2.5 percent that goes to the state.

If legislators agree with the State/County Finance and Revenue Committee, however, that exemption will change.

The committee, created through language in the budget bill in 2016 and made up mostly of legislators and county officials, unanimously voted to authorize the three counties to limit the value of a home that would be eligible for the program. The vote came in September, but members revisited the issue Wednesday and agreed to pass along their recommendations to the General Assembly.

New Castle County Executive Matt Meyer said someone bought a $1.75 million house in the county a few months ago and, because it was the buyer’s first home, he or she was exempt from the county’s portion of the realty transfer tax, “costing” the county around $13,000.

A person buying a million-dollar home is not going to be dissuaded by another $10,000 or so in taxes, Mr. Meyer, a Democrat, argued.

“I don’t understand how you would be opposed to providing some reasonable cap,” he said to Bruce Plummer, president of the Delaware Association of Realtors.

Speaking on the association’s resistance to the proposal, Mr. Plummer noted Americans are buying their first homes later than ever, Delaware is selling houses to fewer first-time buyers and the First State’s high realty transfer tax and foreclosure rate are barriers for potential residents.

“We need to do everything we can to make home ownership more affordable to the masses,” he said.

According to CoreLogic, a financial services company that specializes in real estate, the homeownership rate fell to 63.4 percent in 2016, the lowest mark in half a century.

A cap would only impact a portion of first-time homebuyers — if it is set at, say, $1 million, any house that sells for less is still exempt from the buyer’s share of the tax.

The exemption “cost” Kent County $1.73 million in the fiscal year ended June 30, according to Mr. Plummer.

Even if lawmakers approve the measure, the counties may not even choose to adopt a cap, with officials from both Kent and Sussex expressing uncertainty over the prospect Wednesday.

“I’m not sure Levy Court would entertain it,” Kent County Administrator Michael Petit de Mange said.

The committee also is urging legislators to make a minor change to a tax form that must be filled out for someone selling a property and moving out of state. The recommendation would remove a box that, if checked, indicates the seller is unsure how much they owe to the state in taxes and will pay any required sum later.

“We felt that, as they do in New Jersey and they do it in certain situations in Maryland, they collect it at settlement, so it automatically comes off your settlement, so any fees that the seller has to pay are collected at settlement and when they file their tax returns there’s an adjustment to either get money back or they have to pay more, so this way they don’t move to Montana and we never see them again,” committee Chairman Dennis Greenhouse said.

While he noted he is unsure of how much money the current system may have cost Delaware government, even just “$500,000 is $500,000 the state doesn’t have.”