Nicola Sturgeon has pointed to a fall in reading and writing skills among pupils as evidence that Scotland's education system is not good enough.
Writing in the Daily Record, the first minister also said too many deprived children were still being held back.
And she said it was her "sacred responsibility" to ensure every child was given the same chance to succeed.
The Scottish Survey of Literacy and Numeracy recently said literacy standards in P4, P7 and S2 had fallen.
Last year, the survey flagged up a similar drop in numeracy standards.
The Scottish government has come under pressure from opposition parties over the issue in recent weeks.
Ms Sturgeon said ensuring that the Scottish education system becomes, genuinely, one of the best in the world would become the "driving and defining priority" of her government.
She wrote: "So how are we doing as a country when it comes to education? In seeking to answer that question openly and honestly - as we must do if we are to make real improvements - I disagree with extreme opinions at both ends of the spectrum.
"Those who say Scottish education is failing badly are wrong. But let me be clear - those who say it is good enough are wrong, too."
Fewer children are leaving school with no qualifications and more are leaving with several Highers, including from deprived areas, she said.
"These figures are still not good enough," Ms Sturgeon added.
"Similarly, while more youngsters from our least well-off communities are now going to university, the numbers are still far too low.
"Recent evidence suggests standards of literacy and numeracy in our schools are falling. That is unacceptable."
Ms Sturgeon said she was prepared to make "tough decisions" to improve things, and acknowledged that tackling the problems would "take us well beyond education. But education is vital".
The Scottish Liberal Democrats have previously urged Ms Sturgeon to introduce the "pupil premium" in Scotland similar to the additional funding given by the UK government to schools in England to raise attainment among disadvantaged students.
Responding to Ms Sturgeon's article, Scottish Lib Dem education spokesman Liam McArthur said: "The situation in Scottish schools is happening on the SNP's watch because they took their eye off the ball to focus all their attention on the referendum.
"The danger is that the SNP are now moving too slow to put this right.
"Liberal Democrats have said the top priority should be to give extra help to children from disadvantaged backgrounds to help them get on and achieve their potential. That approach has worked well in England and ends up helping all children in the classroom."
During First Minister's Questions at Holyrood last week, Conservative leader Ruth Davidson said there was a need for a "new system of primary testing" such as there is in Denmark and Ontario, "so that we all can see which schools need help and which schools are leading the way".
Ms Davidson said: "After eight years of this government, until your child is 14 years old, you have no clear idea how good their education is in comparison to the rest of the country."
Scottish Labour has previously accused the Scottish government of a "complacent" approach to education, and has called for more to be done to help pupils from deprived areas.
Announcing her intention to stand for the Scottish Labour leadership last week, Kezia Dugdale said transforming Scotland's education system to make it fairer for all would be her key priority.