A row has broken out between the first minister and NHS bosses after she said she would hold them to account over long waiting lists.
Eluned Morgan said on Sunday that she wanted to pressure health board chief executives, "who are paid significant sums of money", over the care they provide.
But a body which represents Wales' NHS leadership it is like "trying to run the NHS with one hand tied behind your back" when so many patients cannot be discharged into social care.
The Welsh government declined to comment.
On Tuesday the first minister is expected to say what her policy priorities are for the rest of the Senedd term, which ends in 2026.
Last week she said her government would prioritise getting long waiting lists down over radical reform of the health service.
The first minister has talked about focusing on "delivering less" and focusing on the "things that matter to people".
On BBC One's Politics Wales programme last Sunday, Morgan said she was not going to fix the NHS in the next 20 months.
"I think it’s important that we put the pressure on those people who are managing the NHS, who are paid significant sums of money," she said.
"The chief executives of our health boards are paid a quarter of a million pounds a year. Let’s get them to be more accountable for the money that the taxpayers are giving them.
"There are examples where people have really brought down these numbers in some places and in others they are simply not delivering the way they should."
Her comments sparked a robust response from the Welsh NHS Confederation, which represents NHS health boards and their bosses.
Its director, Darren Hughes, said: “The first minister knows all too well from her time as cabinet secretary for health and social care that the NHS is treating more people than ever before and that there are a range of factors impacting on the rate of elective recovery."
He suggested waiting lists could not be considered alone "but as part of the whole health and care system".
All health boards, he said, faced a "huge challenge" in discharging medically fit patients "due to the immense pressures in social care, despite best efforts in joint working with local authority partners".
"In some hospitals 20% of beds are unavailable as patients wait to leave hospital.
"This is like trying to run the NHS with one hand tied behind your back – we’re doing all we can to work with local authority leaders and care providers but the FM must be open about the scale of the challenge and what’s needed to put it right."
Most recent figures for July show that 1,541 patients in hospital in Wales were fit enough to be discharged.
Over the last year, assessment issues were responsible for 41% of these delays and nearly a quarter were due to care home placement arrangements.
Earlier Freedom of Information requests by the BBC found the average delayed time patients were spending in hospital beds was five weeks.
It was calculated that this was costing the NHS £14m a month.
Last August's waiting times figures hit record levels, with those waiting longest - more than a tear and two years - had increased.
Analysis
By Gareth Lewis, BBC Wales political editor
Privately, NHS bosses are disappointed at the tone and language of what the FM said on BBC Wales’s Politics Wales programme.
They feel that she did not properly recognise the enormous impact that the lack of social care has on moving patients efficiently out of hospitals.
Their own language is also quite pointed with the suggestion that Eluned Morgan should have known better because of her time as health and social care secretary.
The new FM has a reputation for speaking her mind, but this is a bruising opening exchange before she’s has even officially outlined her priorities.