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The World Health Organisation said last week that 10 cases of the virus had been reported across the central belt of Scotland, adding a few days later the figure stood at 74 across the UK.
Last week it was revealed that a child from Scotland had been flown by air ambulance to a specialist English hospital for an emergency liver transplant.
On Tuesday, Maree Todd told the Scottish Parliament the number of infections north of the border stood at 13.
But the minister assured MSPs there was no link between the hepatitis and the Covid-19 vaccine, because all of the youngsters - aged between one and 10 years old - had not received a dose of the inoculation.
"Although investigations into the cause are ongoing, we are able to definitively confirm that there is no connection between the Covid-19 vaccination and these cases," she said.
"None of the infected children have received a first dose.
"Whilst I know many will be concerned by this situation, please be assured that Public Health Scotland is working hard to identify the cause and is working closely with health agencies across the United Kingdom and international partners."
Ms Todd told MSPs the cases were "unusual" given they do not appear to have been cause by "recognised strains of the virus", adding that only seven or eight such cases would be expected in a year if there were not another underlying condition present.
"At present, we don't know the cause of the hepatitis - all potential causes are being thoroughly investigated and a number of children have tested positive for adenovirus, which is generally mild but which can, in some rare cases, cause hepatitis," she said.
Ms Todd said the most effective way to stem transmission of adenovirus was "good hand and respiratory hygiene".
"I therefore urge anyone taking care of younger children to supervise hand washing and ensure good hygiene," she added.
Parents were warned to contact health care professionals if they notice signs of jaundice in their children.
When asked by Labour MSP Paul O'Kane to give a timetable for more information to be made public about the cause of the outbreak, Ms Todd was unable to give a specific date, but committed to come back to the chamber with "definitive information" when it was available.
She added that, given reports of cases in the US and EU, the virus was now a "global concern".
It comes after health officials said they had detected more cases Europe and the US.
Last week, British officials reported 74 cases of hepatitis, or liver inflammation, found in children since January.
In a statement on Tuesday, the European Centre for Disease Prevention and Control said additional cases of hepatitis had been identified in Denmark, Ireland, the Netherlands and Spain, without specifying exactly how many cases were found.
It said US officials spotted nine cases of acute hepatitis in Alabama in children aged one to six.