The Health Minister Simon Harris says he hopes that talks on the ownership of the new National Maternity Hospital can be substantially completed by the end of the month.
Mr Harris says he himself will get involved, after meetings this week between officials from his department and the two hospitals.
At the weekend, an estimated 2,000 people
Minister Harris said he is listening to them, but says resolving the ownership issue will not be easy, as currently the State does not own either of the hospitals involved.
He said: "People were marching and they were saying they want 'our hospital' and they were referring to it as 'our hospital'.
"Well, obviously the reality is the current National Maternity Hospital is not our hospital, it is a voluntary hospital shared by the Archbishop of Dublin.
"So I think the people in this country have rightly said they want to see that conversation take place about who owns what within the health service and who is involved in what in the health service."
Minister Harris said he hopes the talks can find a solution to suit everyone.
He added: "The issue of ownership is one that is on the table and needs to be examined, so I expect to meet with the hospitals very shortly, I expect the department to be engaging with them this week and hope to be in a position to have proposals by the end of the month, or certainly progress by the end of the month.
"But it is important to say that everybody needs to play their part here as there are two voluntary hospitals which are not owned by the State as stake here as well."
Mr Harris also repeated his previous view that the new national maternity hospital must be "clinically independent" and free of any influence by "religious doctrine".