Nicola Sturgeon has rejected calls for an immediate roll-out of weekly testing across all NHS staff.
The First Minister was responding to long-running demands to expand routine testing in line with care homes.
The Scottish Green Party, who asked for more surveillance in hospitals as the country braces for winter, said all staff should have been given routine tests months ago.
In a letter, Sturgeon said the Scottish Government is "committed" to routine testing "where it has a clear purpose and can contribute to reducing the risk of transmission".
But she said the plans to develop Scotland's Test and Protect scheme over the next three months are focused on building capacity in the NHS.
"These increases in capacity will primarily be required to meet demand from people with symptoms of Covid - both those infected with Covid, and those with colds or flu, or other illness with similar symptoms and clinical care of patients," Sturgeon wrote.
"However, as testing capacity builds and in line with clinical and public health priorities identified through the review of our testing strategy, we will also extend routine weekly testing of asymptomatic groups in a way which focusses on protecting those most vulnerable to the most harm, including those at highest risk of mortality."
Decisions on testing new groups will be kept under continual review, Sturgeon added.
Scottish Greens health spokeswoman Alison Johnstone, who asked for the roll-out of more weekly testing, had presented evidence for her campaign for more weekly testing back in April.
Today she said: "Despite the fact we are in the grip of a second wave of this deadly virus, the Scottish Government has a complete lack of urgency when it comes the World Health Organisation’s top priority, testing.
"The Scottish Government's own testing review established weekly testing as a priority for Scotland, yet in her letter she says routine testing will only happen if there is a clear purpose. I can't think of a clearer purpose than ensuring our vital NHS staff are protected, are able to work and have greater security that they themselves are not going to be spreading the virus.
"It's still the case that someone working in our hospitals today could have the virus and could be walking about without knowing it. I know this is of great concern to those working to look after us all. They should have been getting weekly tests months ago."
