Details of a series of proposals put to Mr Martin by the Local Authority Members Association, on behalf of some 900 members of city, borough, county councils and town councils, demanding representation on the new health bodies, were revealed at the weekend.
Many of the councillors who are members of the local authority body are prominent figures who hold Fianna Fáil seats on local councils. They seek urgent talks with the minister in a bid to defuse the storm over the moves to exclude councillors from the new set-up.
The demand for local authority representation on the new health bodies is backed by LAMA national chairman Wicklow Fianna Fáil councillor Michael Lawlor.
The general secretary of the association, Longford-based Senator James Bannon said: "We want to discuss with Mr Martin the right of each county council to nominate representatives to the new health boards.
Mr Bannon said LAMA had also effectively rejected in recent correspondence with Mr Martin suggestions that the costs of local authority representation on health boards were "excessive".
"Mr Martin has accepted that the Prospectus Strategy Consultants, who have been involved in a study of the health services, do not consider that over-runs in the health services are due, in any way, to the cost of local authority representatives on the boards," he said.
He said the association has told Mr Martin in its submission that to erode the role of local authority members on the country's new health boards would "fly in the face of real democracy." A full-scale debate by councillors on the new health board structures is planned at a special two-day summit in Galway early next month.