The High Court has heard that the Health Service Executive has not yet admitted full liability in a case taken by terminally-ill woman Emma Mhic Mhathúna, despite assurances from the Taoiseach and the Minister for Health that no woman would have to go to court as a result of the cervical screening controversy.

Lawyers for Ms Mhic Mhathúna and her five children have called on the HSE to confirm whether or not they would be contesting liability in the part of the case relating to an alleged misreading or misdiagnosis of a smear test.

Senior Counsel Patrick Tracey told the court today that despite being given assurances from Taoiseach Leo Varadkar and Tánaiste Simon Coveney earlier this month, they were still having to prepare requests for discovery of documents because liability has not been admitted.

He also told the court the case was urgent and needed a hearing date in June and not July, as had been set down for two other cases that came before the court two weeks ago.

Mr Tracey said this case was unique because they were now also faced with new information that Ms Mhic Mhathúna's previous smear in 2010 had been the subject of an audit and they were only told of this on Monday in documents received from the US laboratory Quest Diagnostics.

This new information affected the preparation of their case and a request for documents but it would not be an issue if they knew liability would not be contested, he said.

Counsel for the HSE Patrick Hanratty told the court that while the HSE was in a position to admit liability in relation to an audit of cervical screening, it was not in a position to admit liability for a misdiagnosis, nor could this be done in the next 24 hours.

He said the HSE had made it very clear that it would do everything in its power to settle the cases through mediation.

Mr Tracey said they had written to the HSE to say they would be relying on statements made in press releases and at press conferences by the Taoiseach and Minister for Health Simon Harris.

Mr Justice Kevin Cross said the HSE was not the State, what seemed to be lost in public discourse was that not all cases of a misdiagnosis could result in an admission of liability.

Judge Cross said that was something that was hard to say but it had to be said. He said it would be unfair to force someone into that position.

However, Judge Cross said it was very important in this case that things were progressed rapidly and said the court would do everything it could to assist with that.

He said it was not the time to make "general statements of policy" on either side.

Lawyers for the US laboratory Quest Diagnostics said a hearing date in 21 days' time as requested by Ms Mhic Mhathúna may not be possible.

Senior Counsel Emily Egan said protocols had been agreed for the handing over of cervical smear slides for examination.

Ms Mhic Mhathúna's case, along with the cases of two other women, were adjourned until tomorrow for a further case management hearing. 

Speaking afterwards Ms Mhic Mhathúna's solicitor Cian O'Carroll said they had been informed that smear tests taken between 2011 and 2013 had been the subject of an audit, but it now appeared that 2010 tests had also been audited and they had not been informed of this until they received records from the US laboratory on Monday.

Mr O'Carroll said this was a matter of concern because the findings were very significant in terms of the degree of upgrading of what they found.

He said it was a matter of concern that those documents were not in the CervicalCheck records.