Town officials in three rural Massachusetts communities said the Social Security Administration notified them this week that it will no longer send representatives to meet locally with seniors and answer their questions, because of security concerns following last week’s deadly shooting rampage in Arizona.

In Palmer and Ware — small towns east of Springfield — and on Nantucket, 30 miles off Cape Cod, town clerks and senior center directors said the federal workers who contacted their towns specifically cited the weekend violence, which killed six people and critically injured US Representative Gabrielle Giffords in Tucson, as the reason for discontinuing the visits.

“They indicated they would not be coming to Palmer, as they have for years, because of what happened in Arizona,’’ said Nancy Talbot, the town clerk in Ware.

Yesterday, however, Social Security officials denied any connection between the shootings and ending outreach efforts in some less populated areas, attributing the changes to budget cutbacks instead.

“There may have been a misinterpretation of the message,’’ said Stephen Richardson, a Boston-based regional spokesman for the Social Security Administration. “In terms of word for word, I wasn’t there, and I don’t know what the words were, but . . . our actions are not related to the tragedy in Arizona.’’

The idea that security precautions were behind the cancellations had baffled local residents, who struggled to see a connection between the mass shooting outside a grocery store Saturday and the low-key question-and-answer sessions held for years in municipal meeting rooms.

“Maybe people are just panicking, but whenever I’ve been there, it’s just a bunch of people waiting to talk to someone,’’ said Diane Auclair, 65, a Palmer resident who used the service to sort out her affairs after her husband died. “It’s going to make it hard on the elderly who don’t have transportation, who will have to take a bus to Springfield.’’

The outreach service, which allowed residents to get answers about their federal benefits without traveling to a Social Security office, brought a representative to the local town hall or senior center three times a month in Palmer, once a month on Nantucket, and every other month in Ware.

Mark Hinkle, a Baltimore-based national spokesman for the Social Security Administration, said the sites, known as “contact stations,’’ give the public a place for face-to-face contact in towns distant from one of the agency’s 1,300 full-service field offices.

There were 2,000 such sites in the 1980s, but budget pressures have slowly done away with most of them, leaving only 500, Hinkle said.

The process of closing down more, including those shut down this week in Massachusetts, is continuing.

He said he did not know how many Massachusetts towns were notified this week that their visits were ending.

“It’s a long, slow contraction that’s been underway for a long time,’’ he said.

The discontinuation of the service in the towns notified this week “has been in the works for months,’’ Hinkle said. “We planned to tell them in the new year, it’s not related to Arizona, and if someone made that leap, it’s simply not accurate.’’

But Catherine Stover, Nantucket town clerk, said officials there were told there was a connection, and that federal officials had ruled out travel because of the shootings on Saturday.

While Hinkle disavowed a direct connection to recent events, he would not completely rule out security as having played a part in the downsizing.

The spokesman acknowledged that officials consider security part of their decision-making process, and may “look at nonsecure sites first in terms of what to close down,’’ for the safety of federal employees as well as other people or employees using municipal buildings.

“I’m not saying that security is not an issue,’’ he said. “It plays a part.’’

Auclair said she found it hard to share such concerns, given that the room in town hall where the meetings were held was “right next to the police department.’’

Local organizers said the sessions are always well-attended, and their discontinuation, for whatever reason, will be felt keenly.

“There are months when we have people lined up most of day, because not everyone can access a computer, and just listening for the prompts on the phone system can be very tiring,’’ Talbot said.

For Nantucket residents, the nearest Social Security office is on the Cape, an hourlong boat ride away.

“We’re pretty distressed,’’ Stover said.

Jenna Russell can be reached at jrussell@globe.com.

© Copyright 2011 Globe Newspaper Company.