Humza Yousaf told the BBC’s Good Morning Scotland that the Scottish Government will “leave no stone unturned” and seek assistance “wherever we can” to prevent the collapse of the health system in coming months.
Covid-19 cases have remained steady across Scotland in recent weeks, falling from a peak of nearly 4,000 recorded last month.
Hospital coronavirus admissions are also down – from 1,107 in late September to 829 reported on Sunday - but the situation in some Scottish Health Boards remains critical.
Soldiers will be deployed to support health workers in NHS Borders and NHS Lanarkshire from tomorrow, following a plea from regional health chiefs last week.
This morning, Jillian Evans, Head of health intelligence at NHS Grampian, told GMS that military support was needed across the health service in Scotland.
Speaking to the show later, Mr Yousaf refused to rule out the option.
“If that request comes in to the Government then of course we look at that favourably,” he said.
"The military have been excellent, when we've asked them to come in and help and assist they did not waste a single second. They've engaged with us and made personnel available, where possible.
"The military is getting these requests from every single Health Board and NHS Trust across the entire United Kingdom, so no doubt they are also stretched, but certainly if a Health Board makes that approach to the Government, then we will certainly look to make an approach to the military for assistance.”
Mr Yousaf said deploying further troops across Scotland to bolster the NHS was “ultimately a decision for for the military”.
"Certainly we will - and I have said this time and time again publicly – we will leave no stone unturned. Whenever we can get assistance from, wherever we can help our NHS with what will be the most difficult winter, I think, in its existence, then we will have to maximise that assistance.”