When they achieved the long-sought renewal of a health care contract with the Veterans Administration in October 2012, Island veterans rejoiced.

The contract allowed veterans to receive care on the Island once a month, where previously they had to travel great distances.

But the contract with the Martha’s Vineyard Hospital has at least one limitation.

Non-life-threatening visits to the emergency room are not covered in the plan, so veterans have to decide either to wait it out until the next primary care visit, or pay a hefty bill out of pocket.

The glitch was a subject for discussion Thursday morning when the state secretary for veterans services paid a visit to the Vineyard. “I don’t think you should get a bill after that, because the VA refused to pay for it,” said Bill Stafursky, an Island veteran. “The contract is flawed in that respect.”

In Secretary Coleman Nee’s first official visit to the Island veterans, he gave an update of the recent activities of his office and asked how he could better serve their needs.

Much of the conversation concerned health care services available to veterans, which have recently been strengthened at the local level but still require some tweaking, veterans said.

Mr. Nee said he would take up the issue with the VA, but had no authority in the matter.

“I will promise I can make a hard case for you,” Mr. Nee said.

He continued to say that there is a trend away from VA hospitals, which often require their beneficiaries to travel, and toward contracting agreements with local health care providers.

In Massachusetts, veterans make up about seven per cent of the population, about 370,000 people. The biggest portion of that group are Viet Nam and Viet Nam-era veterans, who tend to be in their mid-60s. The commonwealth spends more per capita on veterans than any other state, Mr. Nee said.

The state assigns a veterans services officer to each city and town, with the exception of the Island, which has a county-wide officer.

Mr. Nee spoke of services and benefits provided by his office, which have increased with the passage of two bills, the Valor Act and the Valor Act II. Under this state legislation, disabled veterans are eligible for some tax relief and educational and employment support. In a new initiative, the department is working with businesses to act as mentors for veterans who are unemployed and underemployed and seeking career development advice. The opportunity is open to Island businesses.

Mr. Nee said his is the only state agency that gives benefits that are earned. “You fulfilled your end of the bargain,” he told the Island vets. “It’s an earned benefit, I am just paying back the IOU.”

Jo Ann Murphy organized the meeting, which was held at the American Legion Hall in Vineyard Haven and attended by about a dozen veterans. As veterans services officer for Dukes County, Ms. Murphy, well-loved among her clients, registers veterans for benefits and attends trainings to keep up with changes in service delivery.

She can’t be sure of the exact number of veterans on Island, and has previously estimated the number at 400 or 500. But Mr. Stafursky said he thought there were far more.

There are 25 veterans currently receiving services at Community Services, according to associate director Tom Bennett. Some receive individual counseling and some visit his weekly veterans group. Most are Viet Nam-era and post-9/11 veterans.

At the meeting Thursday, veterans expressed almost unanimous preference for locally-based services, which have improved greatly in the past few years.

Still, there is a long way to go, according to some veterans. Dental care is not available to them and property tax abatements do not increase with yearly tax rate hikes.

Kevin Voyer, a veteran who served in the army in the 1970s, said property taxes have more than doubled since he bought his home 15 years ago.

He said after the meeting that he thought the state was probably doing their best to meet veterans’ needs. But he said most of the benefits are provided at the level of the federal government, which doesn’t do enough, he said. He said he wished veterans were provided with the same healthcare plans offered to elected officials.

“The government couldn’t care less about veterans,” he said.