Alex Salmond made the promise after calls were made to hold a public inquiry following two deaths from the disease in the Capital since the outbreak began last month.
The timing of criminal investigations must take precedence over any wider inquiry, he said during First Minister’s Questions.
“Thankfully I can report there has been no new cases in the last couple of days,” he said.
“This is an immensely serious outbreak which has resulted in human tragedy. No stone will be left unturned.”
Labour MSP Sarah Boyack, who called for the inquiry, said lessons must be learned quickly.
She referred to the death of firefighter Ewan Williamson in the same part of the capital three years ago.
“His family and fellow firefighters are still waiting for vital questions to be answered,” she said.
“Can the First Minister promise that local communities will not have to wait that long this time and that we will get a proper inquiry and answers to the questions that are concerning the whole community?”
Investigations centre on a cluster of cooling towers in Wheatfield Road in the south-west of the city.