Minister for Health Stephen Donnelly said that private hospitals "need to do the right thing" and work with the HSE on its winter overcrowding plan.
He said that the HSE and his officials have been talking to the private hospitals "right through the year" about using some of their capacity to relieve pressure on the public system.
Mr Donnelly said that he accepted that private hospitals "need to make a profit", but added that "they are for profit entities and we need their services on behalf of patients".
"What we cannot have is a situation where the profits demanded are too high, this is public money and we need to make sure that money is used to the best effect."
Mr Donnelly said the margin demanded "needs to be reasonable".
His comments come as the HSE's emergency department winter overcrowding plan was cast into doubt, after a private hospitals umbrella group said its members may not be able to provide help set to be sought by the public system.
At its meeting last Monday, the Health Service Executive's emergency department taskforce agreed to ask private hospitals to help ease public hospital overcrowding this winter.
During the meeting the group - which includes senior HSE officials, the Irish Patients' Association, the Irish Nurses and Midwives Organisation and others - was told of a HSE plan to tender for private hospital help from 1 November to 29 February.
This help is expected to involve support for treating non-emergency cases in order to make more space available in public hospitals.
However, in a letter to HSE Chief Executive Bernard Gloster, umbrella group the Private Hospitals Association has cast doubt over the plan.
Correspondence from the PHA's Chief Executive and former Fine Gael TD Jim Daly, which has been seen by RTÉ News, says this is because the PHA believes private hospitals have not been given enough notice of the plan - and instead want a lucrative two or three-year deal.
Citing a recent meeting with the HSE, Mr Daly's letter - which was also sent to Department of Health Secretary General Robert Watt, and Assistant Secretary for Acute Hospitals Oversight and Performance Tracey Conroy - read: "The representatives of the PHA present [at the meeting] made it quite clear to the HSE team that such a proposed procurement framework is unlikely to be successful.
"Initiating engagement with the PHA on this days before publicly advertising such a tender is deeply unhelpful and hugely frustrating.
"The PHA has consistently advised for several years that for any such partnership to work it has to be strategic in nature. This proposed framework is neither strategic nor a partnership.
"The PHA members remain fully committed to assisting the public system but, as we have stated consistently, any agreement to procure capacity needs to be strategic and allow for the private hospitals to plan for additional recruitment and capacity where necessary.
"It is not possible for a private hospital to provide the capacity required by the public system for a four month duration with a couple of weeks' notice coinciding with what is the busiest and most demanding period of the calendar year.
"Staffing these short-term arrangements at such short notice would rely wholly on agency staff which significantly and unnecessarily increases costs and represents poor value for money for the Exchequer."
The letter added: "The PHA has advised the Taoiseach, Minister for Health, secretary general of the Department of Health, assistant secretary generals of the Department of Health, and HSE personnel at every level up to and including yourself [Bernard Gloster] that for the public system to avail of increased capacity within the private hospitals we need a line of sight of the work required over a two to three year period, at a minimum.
"We remain available for immediate and substantial engagement on a strategic partnership that addresses capacity challenges within the public system provided it is strategic, clinically safe, patient centred and partnership focussed."
In two statements to RTÉ News, the HSE said its private hospitals tender will be published in the coming days and acknowledged the value of private hospital help.
"As part of the process a pre-tender briefing was held last week, and the tender document is being finalised.
"In line with HSE procurement policies and procedures, details of the tender document will be available once it is finalised and issued," the first statement on Friday read.
The second yesterday in response to the PHA position added: "We recognise the value of the service from private hospitals in providing additional medical beds.
"These additional beds supported the public healthcare system through the pandemic and last winter's pressure period.
"However, the HSE now needs to formalise the arrangements through a public tender and are also seeking access to surge capacity for the 2023/24 winter period.
"The tender allows for a review next February when arrangements will have been in place for 12 months."
The HSE's latest emergency department overcrowding plan comes as INMO figures show an average of 440 patients were on trolleys every day last week
New HSE guidelines published in July said no more than 320 patients should be on trolleys per day.
Earlier, Sinn Féin health spokesperson David Cullinane said Mr Donnelly needs to engage with private hospitals in relation to the plan.
Speaking on RTÉ's Morning Ireland, he said: "There are lots of health stories and it's because the Minister for Health is not engaging in all of these issues.
"So again, the minister needs to engage with private hospitals. He’s asleep at the wheel when it comes to the Children's Hospital, we have a cost overrun in the Department of Health, which the minister is also responsible for.
"There is examples of good relationships with private hospitals. And I think that their concern is that the approach by the minister and the HSE is always crisis driven and piecemeal and last minute."