Shirley-Anne Somerville said there was “no separate pot of money” to fund an improved pay deal for school staff and that any fresh offer would involve diverting cash from other areas.
Thousands of children across Scotland are facing disruption to lessons later this month after teachers announced the first strike action for almost 40 years.
School staff will stage a mass walkout on November 24, after members of the nation’s largest teaching union overwhelmingly backed industrial action over pay.
The EIS union said 96 per cent of its members had backed a strike on a turnout of 71 per cent, with the first day of action set to be followed by others in the build up to Christmas.
The latest offer from the Scottish Government and council umbrella body Cosla was a 5 per cent pay rise, which was rejected by teachers almost three months ago.
Ms Somerville said she was "absolutely determined" to try to reward staff with a pay rise closer to the 10 per cent being sought by the EIS. But she warned coming up with an improved offer would require “difficult decisions” in other areas.
“We've made it very clear to teachers, and everyone across the public sector, that we have huge sympathy for public sector workers, with high inflation and the cost of living that we have,” she told the BBC.
“But we do also have to bear in mind the reality and the context. The Scottish Government has a fixed budget. It cannot change taxes in the year. Its reserves have been fully utilised.
“If we're looking to fund public sector pay offers, that money has to come from somewhere else in the budget. There is no separate pot of money in the education budget or anywhere else within the Scottish budget to allow these deals to be made.”
The leadership of the EIS held a meeting on Friday to decide a schedule of further strike dates, with the details due to be announced in due course.
The union’s general secretary Andrea Bradley said it was “somewhat positive” that Ms Somerville had promised to try to make an improved offer to teachers.
She said the existing offer fell “far short of inflation” and would amount to an almost 8 per cent real terms pay cut for school staff.
Asked if the union would accept a tiered offer, which would see those on the highest pay receive less of a rise, Ms Bradley said any proposed deal must be made on a “undifferentiated basis”.
She said: “We see it that all of our members work equally hard, all of our members worked equally hard across the course of the pandemic and that was recognised by politicians, by parents, by the wider public, so we do not think any of our members deserve a pay cut.”