Minister for Health Leo Varadkar has said he does not want to set a timeline for the introduction of Universal Health Insurance.
Mr Varadkar said that UHI might take a bit longer than the originally planned date of 2019.
However, he said he believed it would be in place in the next term if the Government is re-elected.
Mr Varadkar said that when it comes in the economy will be recovering and there will be more buoyancy in taxation.
Speaking on RTÉ's Today with Sean O'Rourke, the minister said UHI was still the vision, but he wanted to get it right, and the first step would be a single-tiered system for primary care.
He also said the Health Service Executive will be over budget by between €450m and €500m this year.
Minister Varadkar said the health cuts last year were proven to have been unrealistic and the "fiscal hawks" who had wanted savings did not get them.
He said the health budget was held flat during the three-year term of his predecessor James Reilly.
Minister Varadkar said he would be seeking a budget for 2015 to maintain services at existing levels and would also be looking for funding to allow for some developments.
Mr Reilly had previously defended the Government's plans and denied that it would lead to another version of the two-tier system.
It said access to the health service will be based on need and not the ability to pay.
Mr Reilly said then that the aim of UHI was to end the existing unfair, unequal and inefficient two-tier health system.
Tánaiste Joan Burton said reform in the health system must be done in stages, so that "we can learn lessons of what can work and what we should have caution about".
She said Dutch colleagues have told her that their particular system of universal health insurance took over ten years to put into effect and it turned out to be far more expensive than is really suitable for its taxpayers.
Minister Burton also said she is pleased with the plans to roll out GPs cards first to children under six, then to primary school children, secondary school children, and the over 70s, in stages.
She said the plan must be adaptable and has to take into account that reform often takes a considerable amount of time.
Earlier, the General Secretary of the Irish Nurses and Midwives Organisation (INMO) welcomed Minister Varadkar's vow to tackle the low morale among staff in the health service.
Speaking on RTÉ's News at One, Liam Doran said the INMO welcomed what he said was the "shelving" of UHI in terms of a competitive private model.
Mr Doran said that the first thing the minister should tackle is the recruitment embargo "which is crippling the nursing and midwifery workforce".
He said: "Universal Healthcare is an absolute social human right. It's a measure of a common civilised society. The good news is it's shelved so we might have more time to walk away from a private insurance model which would be a race to the bottom.
"The bad news about shelving it is we continue with a two-tiered, three tiered health system".
His comments were echoed by the Irish College of General Practitioners (ICGP).
ICGP Chair of Communications Dr Darach Ó Ciardha said: "There is a growing manpower crisis in General Practice with new graduates and established GPs emigrating or retiring as a result of uncertainty about their future.
"It is essential to take the manpower issue into account when addressing the related issues of UHI and free GP care."
Speaking on RTÉ's Morning Ireland, Sinn Féin health spokesperson Caoimhghín Ó Caoláin also said the UHI scheme needs to be scrapped and not delayed.
Fianna Fáil health spokesperson Billy Kelleher said his party has serious concerns about the UHI proposals.
He said his party is also calling for the minister to scrap the plans.