The party is also promising to make digital transformation of Ireland's health service a priority if they get into government after the next general election, stating that a lack of political will to fund the change has stalled plans to date.
Ireland's health system has for years been beset by long waiting lists, hundreds of people waiting on trolleys in emergency departments during the winter months, as well as a series of health controversies.
Overruns in the health budget has also been raised as a concern with Public Expenditure Minister Paschal Donohoe working with the Health Minister Stephen Donnelly on this year's overspend.
Sinn Fein health spokesperson David Cullinane said that there had been a lack of a "coherent plan and timeframes" in relation to implementing the universal healthcare plan, Slaintecare.
Mr Cullinane said an alternative health document, published on Friday, laid out his party's plan for what the first year of implementing universal healthcare would entail.
This includes widening out the medical card and reducing charges for attending local injury units from 80 euro to 50 euro.
He added that the cost of implementing a fully universal healthcare system would be at least 2 billion euro, which means that it couldn't be done over a short space of time.
When asked when universal healthcare would be introduced in its entirety, he said it would have to be done in phases.
He said a "Slaintecard" system of entitlements would be introduced as universal healthcare is introduced, which would be developed within a term of government.
Mr Cullinane said: "What we're saying is that we will do our best to deliver as much of it as possible. So I'm not sure that everything will be delivered in one term of government simply because of the cost of it. Yes, it will take two terms of government to get to the final destination."