The Tánaiste has said "the full details" of the secondment of outgoing Chief Medical Officer Dr Tony Holohan to Trinity College Dublin "should" have been put in the public domain "at the outset".
Dr Holohan announced last month that he is taking on a new role as Professor of Public Health Strategy and Leadership at TCD.
Speaking during in the Dáil, Leo Varadkar said Minister for Public Expenditure and Reform Michael McGrath "is not satisifed" and is engaging with the Department of Health at the moment.
"This is not in any way casting aspersions on Dr Holohan," he added. "It is important to follow procedures."
He said it would have been "preferable" if the details of the CMO's secondment to TCD had been disclosed at the outset.
Meanwhile the Department of Health has said that its Secretary General, Robert Watt, has responsibility for "all arrangements in relation to staffing" - including the secondment of Dr Tony Holohan to Trinity College.
In a statement tonight, it said: "The Department, at a senior level made this decision in order to show innovation and lead by example."
It added: "The Department was mindful of the general principles of the Civil Service secondment policy which applies to secondments within the Civil Service."
Arrangements "are underway" between the Department and Trinity College regarding the funding of the post.
Fianna Fáil TD Cathal Crowe today highlighted the fact that the Minister for Health, Stephen Donnelly, "only found out about [the apppointment] on Tuesday night".
He also told RTÉ's Drivetime: "It's not a secondment in how I understand a secondment to be, and all of the detail we have seen in the last 24 hours is that this is open ended while a secondment is typically time specific."
The Clare TD said Secretary General Robert Watt "better be prepared to answer questions" about it.
Earlier, Dr Holohan told the Oireachtas Committee on Health that it is not his intention to return to the CMO role "at any point in the future".
He said his secondment to Trinity College Dublin means he has relinquished his role as CMO.
A TCD spokesperson had said the role is "funded by the Department of Health ... under the same terms and conditions of his existing contract".
The spokesperson said: "Secondments between organisations are a regular and common feature across the civil and public service to encourage inter-departmental and inter-agency cooperation and the sharing of knowledge and skills in the public interest."
The TCD role was not put out to open competition and the university said it "was created with Dr Holohan in mind".
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Dr Holohan told the committee this morning that the Department of Health is committed to the development of public health capacity for the future.
He said: "The third level sector will play a key role in providing thought leadership, critical analysis, research as well as the development of knowledge and skills to better support public health leadership, policy making and public health practice."
He said the department intends that he "lead the development and activities of inter-institutional collaboration between universities and the health sector and to develop stronger links with the WHO (World Health Organization) and agencies of the EU."
Sinn Féin Health spokesperson David Cullinane has called for clarity from Minister for Health Stephen Donnelly and Secretary General at the Department of Health Robert Watt regarding the secondment.
Speaking after Dr Holohan addressed the health committee, Deputy Cullinane said he wished Dr Holohan well on what was a "good role", however he said it was "unfortunate" that the means by which the secondment was arranged had "overshadowed" matters.
The Waterford TD said a role in Trinity College Dublin should be paid for by Trinity College Dublin, and transparency was now required on what had taken place.
The Department of Health has said that the role of Chief Medical Officer will be filled in the usual way for posts at this level, subject to the appropriate sanction from the Department of Public Expenditure and Reform.
Yesterday, Minister Donnelly said he did not sign off on the secondment of Dr Holohan but said he fully supports it.