Then-minister Tony Benn was asked to quit by PM James Callaghan after raising doubts about the 1977 "Lib-Lab pact", National Archives files reveal.
Tony Benn retired from Parliament in 2001 at the age of 76
They show that Mr Benn signed a letter calling for a special meeting of Labour's governing body about the pact.
In a phone call, Mr Callaghan told Mr Benn he had always "sailed close to the wind" but had now "gone to the limit".
Other secret files released include a 1976 letter from Donald Rumsfeld urging the UK not to make defence cuts.
After Mr Callaghan's government became a minority government in March 1977, he made an agreement with Liberal leader David Steel for the two parties to work together to run the country.
The newly-released note describes a telephone call made by Mr Callaghan to Mr Benn at 2000 on Thursday 24 March - a day after the pact was agreed.
It says Mr Callaghan referred to a letter, "which already had 15 signatures", calling for a special Labour National Executive Committee meeting about the pact.
Mr Callaghan - who died in 2005 - told energy secretary Mr Benn he would not expect a Cabinet member to sign without telling him, the note adds.
"Mr Benn said, 'I have already signed it' and the prime minister replied, 'in that case, I must ask for your resignation'," the note continues.
According to the note, Mr Benn - who retired from Parliament in 2001 at the age of 76 - told Mr Callaghan he would "consider his resignation or see if he could withdraw his signature".
James Callaghan became prime minister in 1976
It continues: "Mr Benn added that if he were to withdraw under threat of dismissal, it could become widely known."
Mr Benn ended the talk by making a quip about getting "Steel in and me out".
The note reports that, at this point, "the conversation came to an abrupt end".
Despite their contretemps, Mr Benn - now 82 - remained in his post.
Also released by the National Archives on Friday is a letter from Donald Rumsfeld - during his first spell as US defence secretary between 1975 and 1977 - to UK defence secretary Roy Mason.
In it, Mr Rumsfeld, who served in the same post under President George W Bush from 2001 to 2006, expresses his dismay at planned UK defence cuts.
Mr Rumsfeld served under President Gerald Ford from 1975 to 1977
Referring to Nato's Cold War concerns about the power of the Soviet Union, Mr Rumsfeld stresses "how vital it is that all of us in the alliance avoid public actions and precedents which will create a discordance between the reality of the growing threat and any lack of resolve to meet it".
The letter, dated 19 July 1976, adds: "Any reductions that would weaken or appear to weaken your defences would impinge adversely and directly on the collective security of every ally."
Critics of the current government would argue that Mr Callaghan's Labour cabinet of the time was not as easily influenced by the US as its modern-day equivalent.
On 28 February 1977, Mr Mason's successor as defence secretary, Fred Mulley, announced a £200m defence budget reduction.