Ms Sturgeon came under repeated attack during First Minister's Questions on funding for health boards, closed hospital wards, oncology services and the late opening of new facilities.
Scottish Labour leader Richard Leonard led the criticism, demanding why the children's ward at St John's Hospital in Livingston has not yet been opened on a 24/7 basis.
Highlighting a commitment made by Health Secretary Jeane Freeman earlier this year that the ward would be open at all times by October this year, Mr Leonard said it currently remains closed three nights a week.
However Ms Sturgeon said: "It will be open 24/7 as soon as it is clinically safe for children for it to be so, when the recruitment levels, which have been difficult, reach a level where that ward can be open. I am assuming he's not arguing that that ward should be opened when it is not clinically safe for children."
Mr Leonard responded: "But you knew about these problems seven years ago. Surely by now you should have ensured that this hospital is safe and it is reasonable to have it functioning for children again."
Raising the case of a visually impaired 12-year-old girl from Whitburn who was now having to travel to Edinburgh for out-patient appointments, which was affecting her attendance at school, he said: "Erin may not have a vote yet - but she does have a voice, and she deserves an answer.
"So will the First Minister explain to Erin why she has to miss a whole day of school and why she can’t get an appointment at her local hospital?”
He also warned that child patients and their parents would face “additional cost and stress” travelling long distances for hospital appointments in the winter months, and added: "All the time we have a children’s hospital in Edinburgh costing £1.4 million a month which cannot open its doors until October 2020.”
"Does the First Minister not understand how angry parents and patients, including children, are over her Government’s failure to protect and deliver children’s health services? Isn’t it clear that the SNP cannot be trusted with the NHS?"
Ms Sturgeon replied: "Of course we want Erin to be treated in her local hospital in St John's, but it's vital she gets the best possible treatment. There are recruitment challenges here which are nit unique to Scotland. Our first responsibility and obligation is to make sure that there is clinically safe and high quality care for the young people who need it.
"We'll continue to ensure the investment in our health service that it needs, but we won't shy away from difficult issues, like recruitment challenges, and we will always make sure we are supporting clinically safe and high quality treatment as close to people's homes as possible, but the first priority is patient safety.
"When the SNP came to power a number of hospitals were under threat, the Vale of Leithen for instance, and St John's, and left on the track Scottish Labour were on they probably wouldn't be open now. So we will protect local services, but we will prioritise patient safety."
Meanwhile, Scottish Conservative MSPs Edward Mountain and Liam Kerr raised the issue of finances and services at NHS Highland and NHS Grampian respectively.
In response to Mr Kerr, Ms Sturgeon said: "We are increasing health budgets for health boards across the country.
"And I would just again point to the Conservatives, as I frequently do when issues like spending on health, on education, on justice, or any other matter, are raised - if we followed the strictures and the recommendations of the Conservatives when it comes to setting our budgets, if we had prioritised tax cuts for the richest in our country, instead of extra funding for the National Health Service, our health service right now would have more than £500 million less in its budget than it currently does."
Scottish Liberal Democrat leader Willie Rennie asked the First Minister about NHS Highland, where he claimed patients have been told to "seek treatment elsewhere because Raigmore Hospital is nearly full up".
He said: "After 12 years running our NHS, is the First Minister proud of that record?"
She responded: "Our NHS is seeing more patients than ever before. If you look just at accident and emergency, this is for the country overall, despite the pressures, more people are being admitted, discharged or transferred within four hours in this calendar year so far compared to the previous year.
"We've got record funding, record numbers of staff. Of course, we want to encourage patients to seek help and treatment in the best possible place for them, that is not always in hospital, that's often in primary care or in the community.
"But our health service is doing more than it's ever done before and I think it deserves our grateful thanks for that."
Mr Rennie said: "People rely on the NHS and they are being let down by this Government. Thousands of people are stuck in hospital even though they are fit to go home despite the solemn promise from this Government.
"Audit Scotland say the NHS is critically short of staff, the Royal College of Emergency Medicine say we are hundreds of A&E beds short, and the waiting time guarantee - it's broken every hour of every day. After 12 years in power, has the First Minister got any more excuses?"
Ms Sturgeon hit back at Mr Rennie, telling him: "For a representative of the party that was the co-architect of austerity to get up here and talk about spending in our health service really takes the biscuit."