George Younger feared the political consequences of the extra cuts.
A plan was then hatched between Downing Street and the Scottish Office to find "invisible" savings after Mr Younger said he couldn't make extra cuts straight away.
Letters released under the 30-year rule show Mr Younger was prepared to make the extra cuts, but only if it could be done without it being noticed by opponents.
The messages were exchanged between the Chief Secretary to the Treasury Peter Rees, who wanted more cuts above the £30million over three years offered by the Scottish Office, and the Prime Minister who made it clear she backed the Treasury plan for "larger savings".
In 1984 Mr Younger was getting ready to announce a cut of £5m in the budget for 1985/86 followed by another £5m and then £20m in the next two years.
He was asked for £20m in each of the three years but he said it couldn't be done without critics seizing on it.
When Mrs Thatcher was informed of the discussions she backed the Treasury and asked for more cuts.
The letter, from Mrs Thatcher's private secretary Andrew Turnbull, states: "While she has noted the arguments put forward by the Secretary of State for Scotland on the difficulty of defending slower growth in the Scottish block, she is disappointed, following the meeting on 8 November that the secretary of state does not feel to offer larger savings."
Mrs Thatcher then asked the Lord President to intervene to try to find the extra cuts.
Mr Younger had told Mrs Thatcher he would make savings if they were not too obvious.
A hand written note from Mr Turnbull to the Prime Minister states: "Mr Younger offered to trim something off his block provided it was not too conspicuous."
The note tells Mrs Thatcher of his offer of £30m over three years and the Treasury view it is "meagre". She is asked if she agrees and if Mr Younger should be "urged to move some way towards CST (chief Secretary to the Treasury).
In another letter Mr Turnbull states: "The Secretary of State for Scotland said he was willing to go as far as possible in finding savings so long as these were not visible to informed critics."
It added: "It would be impossible to defend savings which were visible in this way, but was willing to trim the Scottish block programmes as far as possible so long as that could be done invisibly."
A letter from Treasury Private Secretary Janet Lewis Jones explains how the disagreement was resolved - the Scottish Secretary was to discuss with the Treasury "the problems of visibility".