The Taoiseach has called on the secondment of chief medical officer Dr Tony Holohan to Trinity College Dublin to be paused pending a reassessment.
The Government is due to receive a report on the process around the appointment next week.
There is some anger at Cabinet around the move which will see Dr Holohan paid his existing salary by the State despite taking up a new job.
Speaking in Helsinki, Micheál Martin said there has to be full transparency about the move.
“There has to be transparency, there has to be good process and procedure. I don’t see this as just a human resource issue, or a personnel issue in its own right, which I can understand.
“But there was a research perspective to this. There’s a more medium-term perspective to this and in my view it should be paused, there should be a reassessment as to how the objectives that are behind this can be realised in a better and more transparent way.”
Tánaiste Leo Varadkar said: “The Taoiseach has sought a report on this. I don’t think that will take a long time to put together, it might just be a couple of days, and then we’ll be able to decide what to do next.
“It does involve taxpayers’ money and it would appear that it involves an additional expenditure of taxpayers’ money because there will be a CMO and that CMO will be paid, and they’ll also be in this new position.
“Because it creates a new position and therefore a new cost on the taxpayer, that does matter and that’s why the Taoiseach has sought a report on it so that we can assure ourselves that procedures were followed correctly.”
Mr Varadkar acknowledged the process could have been “better handled”.
The Chair of the Oireachtas Committee on Finance, Public Expenditure and Reform John McGuinness has said that the Department of Health Secretary General, Robert Watt, and the Minister for Public Expenditure and Reform, Michael McGrath, will be asked before the committee to answer questions on the secondment of Dr Holohan.
In an interview on Morning Ireland on RTÉ Radio 1, Mr McGuinness spoke of his “serious concerns” about how the secondment of Dr Holohan to Trinity College Dublin was handled by the Secretary General of the Department.
“It is quite a mess within the Department. It shows a certain dysfunction within the department, and we need to clarify it.
"I have serious concerns about how the Department reached the decision in relation to all of this and also the fact that the Minister (of Health) was not informed. Minister McGrath was not informed." - Additional reporting from Press Association