The High Court has lifted a blanket ban on media reporting of a landmark legal action involving children born to a surrogate mother.

The case involves a couple who want their names included on the birth certs of two small children.

The surrogate mother is supporting the couple's application and the case is described as having serious implications in the public interest.

The Attorney General and the Office of the Chief Registrar of Births, Deaths and Marriages are opposing it.

The State opposed applications by lawyers for three newspapers to be allowed report the proceedings.

The Irish Times, Irish Independent and Sunday Times had asked the court "to lift the cloak" of the in camera ruling and allow restricted reporting of the case.

The proceedings opened on Monday before Mr Justice Henry Abbott, who had ruled the media could not report on the case.

However he revised that ruling today and made an order setting out reporting restrictions.

While the evidence from those involved will be heard in private, designated reporters may report part of the proceedings subject to strict reporting restrictions supervised by the court.

The restrictions prevent reporting by Twitter or other social media outlets and also restrain any reporting before 1pm.

Any reporting of the proceedings from after 1pm can also only happen after 4pm. The restrictions were agreed after discussions between lawyers for the newspapers, the State and the applicants.