He said: "They should stay away as a protest at the lack of facilities for riders and spectators for road racing in Northern Ireland," he said.
Mayor of Ballymoney, councillor Bill Kennedy, who is involved in the sport, made the appeal after two of the province's most promising riders died after a crash at the races Glaslough, County Monaghan, on Sunday.
The riders who died were Andy McClean from Coleraine, County Londonderry and Gary Dynes, a father of two from Magheralin, in the same county.
Mayor Bill Kennedy said the only way to improve safety was to have a purpose-built circuit.
He said: "They should stay away as a protest at the lack of facilities for riders and spectators for road racing in Northern Ireland," he said.
Meanwhile, the Northern Ireland Sports Minister, Michael McGimpsey, has extended his sympathy to the families of the two motorcyclists killed.
He said: "I was shocked and saddened to learn this morning of the deaths of Gary Dynes and Andy McClean in a road racing accident in Monaghan yesterday. I extend my deepest sympathy to their families.
"This is another tragic blow for the sport of motorcycle racing.
"It follows the very recent untimely death of Joey Dunlop which brought home to us all that danger and possible tragedy is never far away in what is one of the most spectacular and exciting of sports.
Mr McGimpsey said he was "extremely concerned at the recent loss of life in motorcycle road racing".
"While the future of road racing is, of course, a matter for the sport's governing body, the MCUI, I have this morning spoken to the organisation's road race convenor, Ivan Davidson, to arrange an urgent meeting to discuss the issue."
Meeting was abamdoned
Motorcycle race organisers in Northern Ireland have said they are to consider further safety measures following the deaths.
The two riders to be killed were among five racers injured in a pile-up during the opening lap of the 250cc race at Glaslough, County Monaghan on Sunday.
The race meeting was abandoned after the incident.
The deaths came six weeks after Ulster motorcycling hero Joey Dunlop was killed in a road race in Estonia, bringing the number of Northern Ireland people killed in the sport to seven in 12 months.
The president of the Motorcycle Union of Ireland described the deaths as a "bitter blow" to the sport and extended his condolences to the families of the victims.
Jim Creagh said race organisers had put safety measures in place during the past season but acknowledged these would have to be looked at again.
"We're going to have sit down again. We put certain measures in during this season and we thought we had certainly improved safety. But this is a very dangerous sport.
Mr McClean had been leading the race at the Monaghan track before the pile-up.
He was taken to Middleton Army base by ambulance and airlifted to the Royal Victoria Hospital in Belfast where he died.
Mr Dynes was operated on at Craigavon Area Hospital, County Armagh, but did not survive his injuries.
Denis McCullough, from Dromara, in County Down, was treated for leg and chest injuries.
His condition was described as "comfortable".
Two other riders Darren Lindsay from Lisburn, County Antrim, and Stephen Thompson from Newtownards, County Down, were also involved in the crash, but neither were seriously hurt.