Workplace Relations Commission chief Kieran Mulvey has been asked to step into the row over plans to co- locate the National Maternity Hospital on the site of St Vincent's University Hospital in Dublin.
New Health Minister Simon Harris has appointed Mr Mulvey as a mediator after hosting a joint meeting with representatives from both sides.
The two bodies are at loggerheads because the proposed governance requirements set down by St Vincent's for the new hospital on its grounds in Elm Park will place all services, including tertiary maternity and neonatal services at the National Maternity Hospital, under the control of the St Vincent's board and shareholders, the Religious Sisters of Charity.
Under such an arrangement, the role of the Master of Holles Street, currently held by Dr Rhona Mahony, would be replaced by a single clinical director reporting to a CEO appointed by St Vincent's.
The dispute has all but derailed the entire process, which was first mooted in 1998.
However, Mr Harris told the Herald last night that he wants a speedy resolution.
"Expectant mothers and their children absolutely need a new national maternity hospital," he said.
"While I cannot impose a solution between Holles Street and St Vincent's, I'm very eager to use my position to bring both sides together and pave a way forward.
"I've asked both to engage in a process of mediation. I've been assured by both hospitals that they will approach this in a very positive manner. We need to get on with building this hospital."
Holles Street - the biggest maternity hospital in the country, which last year delivered nearly 9,500 babies - describes its current hospital as "antiquated, under-sized and unsuitable for modern obstetric and neonatal practice".
The Department of Health said there was "unanimous agreement" that a mediation process would be put in place straight away.