New figures show 5-14 attainment levels have increased across the board in reading and writing and at almost every stage in maths.
Mr Peacock said: 'This is welcome news. More pupils are hitting the mark in critical subjects and gaining the foundations for success in later life.
'But we must not be complacent. We want to see attainment continue to improve and be more rigorously assessed. That is why we are consulting on a major overhaul of the assessment system to better support learning and boost attainment.
'New classroom procedures will place a greater emphasis on learning and a new Scottish Survey of Achievement will provide a more comprehensive picture of attainment across the country.'
Today's figures show the percentage of pupils reaching expected attainment levels is:
89.3 per cent at P3 (up 3.5 per cent since 1999)
78.1 per cent at P4 (up 6.4 per cent since 1999)
79.9 per cent at P6 (up 5.7 per cent since 1999)
67 per cent at P7 (up 5.9 per cent since 1999)
55.3 per cent at S2 (up 7.5 per cent since 1999)
Mr Peacock added: 'There is still much work to be done to help our children achieve even higher standards. This is particularly true during the early years of secondary and that is why we have pledged to reduce the size of English and maths classes during this crucial phase.
'There is also a marked difference between the performance of boys and girls and schools will continue to address this gender gap through imaginative classroom practices. At a national level, our move towards a more flexible and relevant curriculum will help ensure schools become more appealing to boys in particular.'
5-14 attainment targets are as follows:
Level A should be attainable by most pupils in P3
Le vel B should be attainable by most pupils in P4
Level C should be attainable by most pupils in P6
Level D should be attainable by most pupils in P7
Level E should be attainable by most pupils in S2
The Executive published proposals for changes to the assessment system in September and these are currently out to consultation.