The rare strain of Staphylococcus aureus affected infants at the Princess Royal Maternity Hospital in Glasgow and was described as “very challenging” by NHS bosses.
Health chiefs vowed to continue screening for the infection, which is spread by body contact.
NHS Greater Glasgow and Clyde announced on 31 January that the two premature babies had died at the Princess Royal Maternity Hospital.
The rare strain of Staphylococcus aureus and affected infants had never been seen in the UK before.
Two premature babies died following the infection, and another became ill.
A fourth baby was treated for the infection, and another four infants had the bacteria on their skin but did not require treatment.
Charity SANDS (Stillbirth and Neonatal Death Society) attended a meeting with the health board at the Queen Elizabeth University Hospital.
Campaigner for SANDS, Jean Anne Mitchell, said: “I’m absolutely shocked and horrified to find that babies in our neonatal units are dying of Staphylococcus, which is a bloodstream infection caused by body to body contact.
“When you have more than one baby that has died... one baby is one baby too much.
“Parents cannot move forward.
“There must be an audit trail of staff who dealt with these babies.
“Staff are going from unit to unit to cover gaps.
“We must get answers and we must be accountable.
“If my baby was being cared for in a neonatal unit I would expect that everything was being done to make my baby better and not for someone to not have done something to give my baby the best chance to survive.
“I was horrified to hear that the comment from NHSGGC that you were going to have to speak to visitors coming to unit.
“Parents who are already suffering, the last thing they want to know is that they may have done something to cause this.”
Dr Jennifer Armstrong, Medical Director of NHSGGC said: “This has been a challenging infection to bring under control.
“For this particular strain, it was the first time it has been seen in the UK.
“We worked very closely with England and that does mean screening all parents, all staff and all visitors who come into the unit.
“It’s been a very, very robust process “We are still screening babies and we will continue to do so until we are absolutely certain that it is out of our hospitals.”
A spokesman for NHS Greater Glasgow and Clyde said: “We have already confirmed that we had identified an extremely rare strain of staphylococcus aureus (type 11164) at the Princess Royal Maternity Hospital (PRMH).
“This strain is highly resistant to the two antibiotics normally prescribed for Staphylococcus. Aureus and is also resistant to the skin cleaning agent routinely used in hospitals across the UK.
“It has been confirmed that this is the first time this strain of bacteria has been identified in Scotland; previously these cases have only been identified in two other countries worldwide (Germany and China).
“We have continued to screen babies in our three neonatal units and have also put in place a number of further infection control measures including staff screening, the prescribing of different antibiotics and the introduction of a new skin cleaning agent.
“No further patients have tested positive for Staphylococcus aureus infection.”