The relatives arranged the anniversary vigil before the prospect of Ms. Gilbert’s discovery was even raised: On Dec. 13 of last year, officials reported the discovery of four bodies in the brush on Jones Beach Island.

The authorities have maintained, though, that Ms. Gilbert’s case is not necessarily related to the others. The location of the body believed to be hers, Mr. Dormer said Tuesday, has helped validate his belief that Ms. Gilbert drowned while trying to reach the parkway through the swampland nearby after knocking on a door in Oak Beach. The body was found, Mr. Dormer said, about a quarter mile northeast of where investigators last week retrieved what they believed were Ms. Gilbert’s purse, jeans, shoes and cellphone.

“She traveled at least half a mile, three quarters of a mile, on foot through that muck,” Mr. Dormer said at a news conference on Tuesday. “It would be very easy to get exhausted and fall down and not be able to move any further.”

Later, Mari Gilbert, Shannan’s mother, appeared at the vigil with a small group of friends and relatives of the other victims. Those gathered released balloons into the air, recited the Lord’s Prayer and, in some cases, hammered crosses into the earth beside the parkway.

But Mari Gilbert, who said the authorities contacted her on Tuesday morning with news of the discovery, was unconvinced that the remains were her daughter’s, noting that an autopsy had not been completed. “Until I hear positive confirmation that it’s my daughter, I’m going to believe it’s not,” she said.