Jeane Freeman is scheduled to appear before MSPs later this month to explain the rising number of serious incidents at the Queen Elizabeth hospital in Glasgow.
However, following reports of a third child death, and intensifying calls from parents for answers, both the Scottish Conservatives and Scottish Labour have demanded the health secretary make a statement to Parliament on Tuesday.
Tory health spokesman Miles Briggs said there was a cover up surrounding the deaths of children linked to a contaminated water supply, and that Ms Freeman needed to reassure patients at the hospital that the environment is safe.
Mr Briggs said: "My thoughts and condolences are with the family at this unimaginably difficult time. Families need to be told the truth as to what has happened at the Queen Elizabeth University Hospital and from the outset that is what I have sought to achieve.
"Jeane Freeman has to make a statement on this growing scandal on Tuesday. The families of those children affected by this simply cannot afford to wait any longer for answers.
“We need to know exactly what’s going on at a hospital the SNP planned, built and now runs. It’s simply not good enough for the health secretary to punt this into the long grass.
“There is now real concern among patients, their families and staff that this isn’t just a historic issue, and many simply don’t trust the hospital to provide care safely.”
He added: "The crisis engulfing the Queen Elizabeth University Hospital is totally unacceptable. It’s time for the First Minister to take charge and step in to demonstrate the government are actually in control and can provide answers to the safety concerns parents and families are expressing.”
Scottish Labour's health spokesperson, Monica Lennon said the news of another death was "tragic" and added: "My thoughts are with the child’s family at this very sad and difficult time.
“Health Secretary Jeane Freeman must return to Parliament on Tuesday and provide an urgent update. The public will rightly question why a child who contracted a hospital-acquired infection has died so soon after the health board insisted the hospital is safe.
"It must be established if the infection was linked to the water contamination scandal and an independent team should be brought in."
NHS Greater Glasgow and Clyde was placed in special measures after being accused of covering up the deaths of children who picked up infections at the hospital. It is understood the latest patient to have died was moved between various wards before their passing.
The culture of the board was described as "rotten at the core" by Scottish Labour's Anas Sarwar, who along with Ms Lennon, yesterday met with the parents of children receiving treatment at the site.
Mr Sarwar had previously received a leaked report from a whistleblower indicating that issues of water contamination were pervasive at the hospital in 2017 and 2018. The death of 10-year-old Milly Main in August 2017 after she had beaten cancer has been linked to an infection caused by contaminated water at the site, and there have been questions raised about the death of three-year-old Mason Djemat who died just weeks before Milly.
Another leaked report last week also showed that Greater Glasgow and Clyde board was told areas of the flagship £800 million campus were at a "high risk" of infection before it opened in 2015.
The Herald on Sunday newspaper has now reported that a young patient who was receiving treatment contracted a hospital-acquired infection and died earlier this week.
A statement released by a group of 15 parents, who met with Anas Sarwar and Monica Lennon MSPs yesterday, said they have no confidence in the board and believe it is not fit for purpose, adding those responsible should not remain in place while an investigation is carried out.
They also asked whether the site is safe and why their children being given prophylaxis antibiotics - which is said to increase the risk of resistance and other side effects.
Mr Sarwar said: "It's clear that the culture is rotten at the core of the health board. It's clear that there is a culture there of silencing, of bullying and intimidation.
"One thing that needs to be remembered is that none of this would have potentially come to light if it wasn't for the whistleblower putting their head above the parapet and risking their own job and sharing the information with me.
"It should not rely on a whistleblower, it shouldn't rely on MSPs, it shouldn't rely on a free press, although that's all important, to get truth and answers about what's happening in our National Health Service and to get transparency for and answers for the parents, but that's what's happened in this case.
"I honestly don't believe that the health board would have acted appropriately if we hadn't gone public. These are issues that have been raised with management for years and they have failed to act."
Ms Lennon said the statement from the families should leave Ms Freeman in "no doubt that families feel completely failed."
She added: “Allowing the current leadership team to investigate themselves is not tenable. SNP ministers took stringent action against health chiefs in Tayside over financial mismanagement; the scandal at Greater Glasgow and Clyde concerns patient safety, and a number of deaths are under investigation. Jeane Freeman must explain how bad it needs to get for her to take maximum action.”
However Mr Sarwar said he believes Ms Freeman had been "kept in the dark" over the extent of issues at the site.
"I find it completely unbelievable that the reports that I presented in Parliament on Thursday showing that they knew the water supply was not safe and there was high risk back in 2015 and again in 2017, and then again in 2018, that it was the first time that Jeane Freeman had ever seen these documents and didn't know they existed.
"If that was a health board being transparent, being open, given what's happened in the last few weeks, they should have shown that to the Cabinet Secretary and they should have been open and transparent about it.
"The fact that they weren't show that there's still a culture of cover-up, a culture of bullying, a culture of intimidation, and a culture of silences."
The Scottish Labour MSP has called on the management at the board to step aside in order to have a truly independent investigation into the infections at the hospital campus.
Mr Sarwar added: "Whilst these people remain on the scene, they compromise the investigation and also they compromise the trust in whatever the investigation comes out with."
NHS Greater Glasgow and Clyde said that it is bound by rules of patient confidentiality when asked about the report of the death this week.
"We need to take care when discussing individual cases as we are bound by strict rules of patient confidentiality," said a spokeswoman for the board.
"The issue is being appropriately managed and Health Protection Scotland has been informed. As this involves a single case, we have no further comment to make."
A Scottish Government spokesperson said: “We are committed to ensuring that matters relating to the Queen Elizabeth Hospital are dealt with transparently and with clear accountability.
"That is one of the reasons the Health Secretary has instructed a public inquiry to be chaired by Lord Brodie. The decision by Health and Social Care Management Board to escalate the board from stage 2 to 4 on the performance framework was in recognition of the need for decisive action.
"The Health Secretary has already committed to updating Parliament.”