The Minister for Health Simon Harris has said he hopes to see significant reductions in waiting lists in the coming months.
Mr Harris said the HSE has informed him they would reach a target of ensuring no child with scoliosis will have to wait more than four months for surgery by the end of this year.
"I expect everyone to be offered a form of treatment to comply with the four-month target," he added.
Speaking on RTÉ's This Week programme, the Minister said he would enter one caveat to this and it applied to parents offered treatment abroad and for whom this was not a viable option.
Asked if the HSE would reach a target to reduce the numbers waiting more than 15 months for outpatient appointment and day case procedures by 75% by the end of October, he said: "That's the target the HSE set, that's the target the HSE were funded for and I expect them to deliver it."
The Minister added: "I hope so, we've to wait until we see the data. The indications I have is that [the] number of people waiting on operations has fallen this month. I expect, based on work being done by HSE and National Treatment Purchase Fund, we will see a further fall this month.
"Last month we saw a reduction of 2,100 patients waiting for operations in this country.
"I expect we will continue to see reductions this month and right on throughout the year as we have now re-activated the National Treatment Purchase Fund and are now investing in waiting lists.
"People are waiting far too long in this country," he said.
Mr Harris pointed out that 353,000 patients were offered out-patient reviews and did not show up. He said this was not a criticism of the patients but of the system.
However, he said the media never refer to this figure to provide a wider context for the waiting lists issue.
In relation to the new GP contracts, Mr Harris said he hoped to be able to progress extending free GP care to all those aged under 12 next year.
But he added the negotiations also required him and the Government to address issues of concern to GPs.
In relation to the Sláinte care report on the future of the health services, the Minister said he would establish an implementation group by the end of the year.
He said the Government would provide transitional funding, over a number of years, in addition to existing spending to help progress the move to a new health system with the emphasis on primary care.
Later the Minister announced a new National Treatment Purchase Fund initiative to provide diagnostic endoscopy tests to an extra 700 patients who are waiting for scopes. It will cost €700,000.
