The head of the Health Service Executive, Prof Brendan Drumm, has been invited to a meeting of Fianna Fáil TDs and Senators in Leinster House to discuss the party's concerns about continuing problems in the health sector.
It follows complaints by members of the main Government party about a perceived lack of accountability from the HSE and difficulties in obtaining information from the body.
TDs have complained that it is taking weeks and months to elicit responses to parliamentary questions about specific queries.
The complaints were raised by members of Fianna Fáil's parliamentary party during a special meeting with Minister for Health Mary Harney in Leinster House on Wednesday evening.
Thirty-four TDs and Senators spoke during the meeting which was described as good humoured and positive by both Ms Harney and the chairman of Fianna Fáil's health group, John Moloney.
The TDs and Senators agreed to invite Prof Drumm to a similar meeting in the coming weeks to address the specific queries of TDs and concerns about the lack of information coming to them from the HSE.
Yesterday a spokesman for Mr Drumm said he would be happy to accept the invitation and that the issue of democratic accountability was taken very seriously by the HSE.
"Prof Drumm is willing to engage with any stakeholder group," the spokesman said, pointing out that he had recently addressed the Progressive Democrats annual conference and had also addressed a meeting of Fine Gael TDs.
The spokesman said delays in compiling replies to Dáil questions were being addressed by the HSE and regional forums had also been established.
Fianna Fáil TDs are the latest to complain about access to information from the HSE and compare it with the previous situation with the old health boards, where elected representatives held seats on the board and had direct access to information and officials.
During Wednesday's meeting with Ms Harney, most of the politicians spoke about specific local issues affecting their constituents including facilities and services.
A number of TDs, including Noel O'Flynn of Cork North Central and John McGuinness of Kilkenny, said there were concerns that the problems in the health sector were having a negative effect in every constituency.
Improvements in A&E services, a reduction in the numbers on hospital waiting lists, and care for the elderly were also highlighted as being of critical importance before the next general election.