Two premature babies have died after contracting a bloodstream infection at a Glasgow hospital, the third infection-control crisis to hit the city’s health service within two weeks.

NHS Greater Glasgow and Clyde confirmed on Wednesday night that it was investigating three cases in the neonatal unit at the Princess Royal maternity hospital. It said the infection was “one of a number of contributing causes” in the deaths of two “extremely premature” babies, and that a third had required treatment and was in a stable condition.

On Tuesday Scottish prosecutors confirmed they were investigating the deaths of two patients, a 10-year-old boy and a 73-year-old woman, who contracted an infection connected to pigeon droppings at Queen Elizabeth university hospital in Glasgow. Another patient at that hospital remains seriously ill after contracting a separate fungal infection called mucor.

Dr Barbara Weinhardt, an infection control doctor, said a number of measures had been taken at the Queen Elizabeth university hospital, including a deep clean, isolation and barrier nursing, safety briefings to all staff and infection control advice to all visitors.

She said: “Our thoughts are with the families affected. Results have confirmed that the three cases of Staphylococcus aureus are linked and our investigations continue into how they are linked.”

Dr Alan Mathers, chief of medicine, women’s and children’s service for NHS Greater Glasgow and Clyde, said an incident management team meeting was convened last Thursday.

“The IMT began their investigations into possible linkages between the three cases and sent samples for testing. Whilst these results were awaited, we spoke to the families affected, together with the parents on the unit and staff, to let them know of our investigations. The results that have come back have confirmed links between the three cases,” he said.

“Our infection control team continues to work closely with clinical colleagues and domestic staff to manage the situation and take all necessary steps to maintain patient safety.”

The Scottish Liberal Democrats’ health spokesperson, Alex Cole-Hamilton, said the past few weeks had highlighted “significant vulnerabilities” in the Scottish healthcare system.

He said: “This is a desperately sad situation and my heart goes out to the families affected. As soon as she is in possession of all the facts, the health secretary should appear before parliament to offer reassurances to patients that these outbreaks are being addressed and that where necessary procedures will change to prevent any further tragedy of this kind.”

Asked about the neonatal deaths at first minister’s questions in the Holyrood chamber on Thursday, Nicola Sturgeon passed on her condolences to the families of the babies who died, and insisted that the health board was “taking all necessary steps to maintain patient safety”, including regular screening of newborn children and enhanced cleaning.

She added that the board has asked Health Protection Scotland to carry out an investigation, but added that the Staphylococcus aureus bacterium linked to the deaths is “regrettably not uncommon”.