Ken Clarke told Margaret Thatcher Britain should just "blow up a few ships" over the Falkland Islands, while another Tory MP warned her his "constituents wanted blood", according to newly released files.
Clarke, then a junior minister, along with Sir Timothy Raison, MP for Aylesbury, said: "Hope nobody thinks we are going to fight the Argentinians. We should blow up a few ships but nothing more."
Lady Thatcher marked the comment with two blue biro lines.
The private papers from 1982 reveal wide divisions within the Conservative party over how the government should respond to Argentina's invasion of the Falklands.
While the Tories publicly presented a united front, briefing notes prepared for the prime minister demonstrate the polarised opinions she had to contend with in the early days of the crisis.
A hand-written note by Lady Thatcher also shows how she grappled with her response to the Duke of York's deployment as part of the Falklands task force.
Prince Andrew's place on board the HMS Invincible aircraft carrier provoked concern at the time because of the possibility of the Queen's son being killed in action.
However the Queen insisted that her son remained on the ship and he went on to fly missions as a Sea King helicopter co-pilot.
The private note reveals several crossings out and amendments.
"If asked about Prince Andrew it is the express wish of The Queen, the Duke of Edinburgh, and of Prince Andrew himself, that if the Invincible sails he sails with her," she wrote.
The deleted passage begins "I should not withhold consent".
This itself has been amended to "I cannot withhold consent" before again being crossed out.
The words which follow are difficult to decipher but end: "our courage are priceless assets which our Royal Family has (sic) themselves in abundance."
Lady Thatcher prepared the note for her own consumption and at that time had no reason to believe it would ever be made public.
It is not therefore thought the crossing out represented any significant change of heart, rather that it indicates her desire to ensure she delivered the correct message.
Historian Chris Collins, from the trust, said the papers reflected how Mrs Thatcher grappled with the turbulent situation.
He added: "These papers reveal how stressful this situation was, it was a massive undertaking which tested her to the full.
"In the early days of the conflict there was great confusion and doubt on behalf of the party and more widely.
"People were feeling very down about the whole process and what was going to happen next. There was tremendous chaos.
"But of course a party has to show a united face as far as it can."
Lady Thatcher is the first British prime minister whose private and official papers have been released in this way.
Charles Moore, her authorised biographer, said: "The Thatcher archive is a marvellous resource for all those interested in her career as prime minister and in this country's recent political history.
"This release will provide the raw material to help researchers study and understand the changing political landscape of her first year as prime minister."
The latest release is open to the public at the Churchill Archive Centre in Cambridge and online at www.margaretthatcher.org