Gardaí from the Donegal Division arrested a 56-year-old man this morning in relation to the investigation.
Cllr Fullerton was murdered in his home in Buncrana on May 25, 1991.
A Garda spokesperson said: “The man was arrested shortly after 10am and is currently detained under Section 30 of the Offences Against the State Act, 1939 as amended, at Letterkenny Garda Station.
“Gardaí invite anyone with any information in relation to this murder to contact the Garda Confidential Line on 1800 666 111.”
In May, Sinn Féin leader Mary Lou McDonald called for an independent public inquiry into the murder.
In a video tribute to Cllr Fullteron to mark the 30th anniversary of his killing, Ms McDonald, said he had “embodied what it means to be a proud Irish republican activist and a dedicated united Irelander.
“Everything he did was about lifting people up and moving forward,” she said.
Cllr Fullerton was the first Sinn Féin member to be elected to Donegal County Council.
The local politician left behind his wife, Dinah Fullerton and his daughter, Amanda and sister, Winnie Noone.
In May, Dinah spoke in the video, describing how happy her husband had been on the day he was killed.
He had been elated that a multimillion euro dam had got the green light for the community.
“The people of his community meant so much to him,” she said.
Three decades after the murder, Cllr Fullerton’s daughter Amanda also spoke in the video, saying she felt hopeful about the future and that her family’s campaign for justice had “overcome boundaries”.
She added: “The timing is good, we’ve persisted. We feel quite confident and resilient as a campaign entity to bring this to its conclusion.”